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Slide 1 www.kostic.niu.edu Reflections on Real (Thermodynamic) Entropy, Disorder and Statistical Information Entropy – (Lecture IV) Prof. M. Kostic Mechanical.

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1 Slide 1 www.kostic.niu.edu Reflections on Real (Thermodynamic) Entropy, Disorder and Statistical Information Entropy – (Lecture IV) Prof. M. Kostic Mechanical Engineering NORTHERN ILLINOIS UNIVERSITY Institute of Engineering Thermophysics Tsinghua University Tsinghua University Beijing, China, June 20, 2013 Beijing, China, June 20, 2013

2 Slide 2 www.kostic.niu.edu Some Challenges in Thermoscience Research and Application Potentials Energy Ecology Economy Prof. M. Kostic Mechanical Engineering NORTHERN ILLINOIS UNIVERSITY Tsinghua University, XJTU, and HUST China 2013: Beijing, Xi’an, Wuhan, June 14-28, 2013

3 Slide 3 www.kostic.niu.edu 3 Hello : Thank you for the opportunity to present a holistic, phenomenological reasoning of some challenging issues in Thermo-science. Discussions are informal and not finalized yet. Thus, respectful, open-minded arguments, and brainstorming are desired for better comprehension of tacit and often elusive thermal phenomena.

4 Slide 4 www.kostic.niu.edu Among distinguished invites were five keynote speakers from China and seven international keynote speakers: three from the USA and one each from Japan, United Kingdom, Singapore, and Spain; including four Academicians and six university Presidents/vice-presidents. It has been my great pleasure and honor to meet Prof. ZY Guo and other distinguished colleagues, and even more so to visit again and meet friends now!

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7 Slide 7 www.kostic.niu.edu Entropy, the thermal displacement property, dS=dQ rev /T (or dQ cal /T) with J/K unit, is “ a measure” of thermal dynamic-disorder or thermal randomness, and may be expressed as being related to logarithm of number of “all thermal, dynamic-microstates”, or to their logarithmic-probability or uncertainty, that corresponds, or are consistent with the given thermodynamic macrostate. Note that the meanings of all relevant adjectives are deeply important to reflect reality and as such it has metaphoric description for real systems. Q cal =Q rev +W loss =Q rev +Q diss

8 Slide 8 Persistent misconceptions : Persistent misconceptions existing for many years in different fields of science. They are sometimes encountered in the scientific and especially, the popular-science literature. The Entropy (2 nd ) Law misconceptions are: 1.The first 1.The first misconception: Entropy is a measure of any disorder. 2.The second 2.The second misconception: Entropy (2nd) Law is valid only for closed systems. 3.The third 3.The third misconception: Entropy (2 nd ) Law is valid for inanimate, not for living (animate) systems. 2009 January 10-12 © M. Kostic

9 Slide 9 : The Boltzmann constant is a dimensionless conversion factor : 2009 January 10-12 © M. Kostic

10 Slide 10 www.kostic.niu.edu …thus thermal & mechanical energies are coupled 2

11 Slide 11 www.kostic.niu.edu Importance of Sadi Carnot's treatise of reversible heat- engine cycles for Entropy and the 2nd Law definitions: Carnot's ingenious reasoning of limiting, reversible engine cycles allowed others to prove that entropy is conserved in ideal cycles (Clausius Equality - definition of entropy), that entropy cannot be destroyed since it will imply supper-ideal cycles, more efficient than reversible ones, but is always irreversibly generated (overall increased) due to dissipation of any work potential to heat (Clausius Inequality) in irreversible cycles. These are easily expanded for all reversible and irreversible processes and generalization of the 2nd Law of Thermodynamics.

12 Slide 12 www.kostic.niu.edu Thermal energy versus Internal energy concepts in Thermodynamics: The entropy is related to internal thermal energy (obvious for incompressible substances), but is more subtle for compressible gases due to coupling of internal thermal energy (transferred as heat TdS) and internal elastic-mechanical energy (transferred as work PdV). Entropy is NOT related to any other internal energy type, but thermal (unless the former is converted/dissipated to thermal in a process).

13 Slide 13 www.kostic.niu.edu Disorder versus Spreading/Dispersal as statistical metaphorical-concepts of entropy: The three terms are qualitative and metaphorical concepts related to each other and have to relate to the random, complex thermal motion and complex thermal interactions of material structure, like its thermal heat capacity and temperature, among others. Only for simple ideal gases (with all internal energy consisting of random thermal motion and elastic collisions), entropy could be correlated with statistical and probabilistic modeling, but has to be and is measured for any and all real substances (regardless of its structure) as phenomenologically defined by Clausius (dS=dQ rev /T abs ). Thus entropy and the Second Law are well defined in classical Thermodynamics

14 Slide 14 www.kostic.niu.edu Disorder versus Spreading/Dispersal as statistical metaphorical-concepts of entropy: The simplified simulations (analytical, statistical, numerical, etc.) should not take precedence over phenomenological reality and reliable observations, but to the contrary: Substance is more important than formalism! ‘Extreme’ judgments based on simulations are usually risky, particularly if detached from reality-checks or with attempt to suppress reality.

15 Slide 15 www.kostic.niu.edu A system form and/or functional order/disorder: A system form and/or function related order or disorder is not thermal-energy order/disorder, and the former is not the latter, thus not related to Thermodynamic entropy. Entropy is always generated (due to ‘energy dissipation’) during production of form/function order or disorder, including information, i.e., during any process of creating or destroying, i.e., transforming any material structure. Expanding entropy to any disorder type or information is unjustified, misleading and plain wrong.

16 Slide 16 www.kostic.niu.edu Disorder versus Spreading/Dispersal as statistical metaphorical-concepts of entropy: There is a "strange propensity” of some authors involved with simplified statistical interpretation of complex, random natural phenomena, to make unjustified statements that their analyses are true descriptions of natural phenomena and that the phenomenological definitions are deficient and misleading, or even worse, that the natural phenomena are a subset of more general statistical theory, for example, that information entropy is more general than thermodynamic entropy, the latter being a subset of the former. For example, some “promoters” of statistical descriptions of entropy become so detached from physical reality as if not aware of the reality.

17 Slide 17 www.kostic.niu.edu Entropy refers to dynamic thermal-disorder of its micro structure (which give rise to temperature, heat capacity, entropy and thermal energy. It does not refer to form-nor functional- disorder of macro-structure: For example, the same ordered or piled bricks (see above) at the same temperature have the same entropy (the same Thermodynamic state)! Entropy and Disorder … S=S(T,V) not of other type of disorder: If T left =T right and V left =V right  S left =S right

18 Slide 18 www.kostic.niu.edu Disorder versus Spreading/Dispersal as statistical metaphorical-concepts of entropy: Since entropy is directly related to the random thermal motion of a system micro (atomic and molecular) structure, it is suitable to statistical analysis, particularly of simple system structures, like ideal gases, consisting of completely randomized particle motion in thermal equilibrium, without any other particle interactions, but elastic, random collisions of material point-like particles. For more complex, thus all real systems, the thermal motion and interactions are much more complex, thus the statistical analysis is metaphorical only and cannot be quantitatively reduced to physical entropy, the latter well- defined and measured in laboratory for all substances of practical interest.

19 Slide 19 www.kostic.niu.edu S gen Entropy Generation (Production) is always irreversible in one direction only, occurring during a process within a system and stored as entropy property. Entropy cannot be destroyed under any circumstances, since it will imply spontaneous heat transfer from lower to higher temperature, or imply higher efficiency than the ideal Carnot cycle engine Entropy Generation (Production)

20 Slide 20 www.kostic.niu.edu Dissecting The Second Law of Thermodynamics: It Could Be Challenged But Not Violated Prof. M. Kostic Mechanical Engineering NORTHERN ILLINOIS UNIVERSITY Carnot 1824 Heat Engine Reversibility Clausius 1850 NO Heat from cold to hot 1865 Entropy Kelvin-Planck 1848 Abs. Temperature 1865 NO Work from single reservoir Gibbs 1870’s Entropy, Chem.Potential Phys.Chemistry Royal Institute of Technology - KTH Presented at: Royal Institute of Technology - KTH KTH Department of Energy Technology, Stockholm, Sweden, 22 May 2012 … with some updates

21 Slide 21 www.kostic.niu.edu Sadi Carnot’s far-reaching treatise of heat engines was not noticed at his time and even not fully recognized nowadays Sadi Carnot laid ingenious foundations for the Second Law of Thermodynamics before the Fist Law of energy conservation was known and long before Thermodynamic concepts were established. In 1824 Carnot gave a full and accurate reasoning of heat engine limitations almost two decades before equivalency between work and heat was experimentally established by Joules in 1843

22 Slide 22 www.kostic.niu.edu Fig. 1: Similarity between an ideal heat engine (HE) and a water wheel (WW) (instead oh heat, entropy is conserved).

23 Slide 23 Carnot Efficiency … www.kostic.niu.edu “The motive power of heat is independent of the agents employed to realize it; its quantity is fired solely by the temperatures of the bodies between which is effected, finally, the transfer of the caloric.”

24 Slide 24 www.kostic.niu.edu Fig. 2: Heat-engine ideal Carnot cycle : Note thermal and mechanical expansions and compressions (the former is needed for net-work out, while the latter is needed to provide reversible heat transfer).

25 Slide 25 www.kostic.niu.edu Fig. 3: Reversible Heat-engine (solid lines) and Refrigeration Carnot cycle (dashed lines, reversed directions). Note, W H =W L =0 if heat transfer with phase change (compare Fig.2).

26 Slide 26 ` www.kostic.niu.edu Fig. 5: For a fixed T H, T Rref, Q H, and Q Ref, the Q(T) is proportional to Q Ref (efficiency is intensive property) and an increasing (positive) function of T for a given T Ref (thus absolute temperature). The Carnot ratio equality above, is much more important than what it appears at first. Actually it is probably the most important equation in Thermodynamics and among the most important equations in natural sciences. T=T Any

27 Slide 27 “Definition” of Temperature, Mass, etc… www.kostic.niu.edu The Carnot ratio equality above, defines Temperature vs. Heat-flux correlation, the way the Newton Law defines Force vs. Momentum-flux correlation. The two simplest non-zero positive-definite functionals are chosen, however the others are also possible. Similarly, the Einstein’s theory of relativity concept could have been correlated with similar, but different functional, resulting to similar and equally coherent theory!

28 Slide 28 Clausius (In)Equality www.kostic.niu.edu

29 Slide 29 www.kostic.niu.edu Fig. 7: Heat engine ideal Carnot cycle between two different temperature heat ‑ reservoirs (T H >T L and W>0) (left), and with a single temperature heat ‑ reservoirs (T H =T L and W=0, ideal reversible cycle) (right). Low-temperature thermal compression is needed (critical), not the mechanical (isentropic) compression, to realize work potential between the two different temperature heat ‑ reservoirs, due to internal thermal energy transfer via heat (W=Q H -Q L >0). The isentropic expansion and compression are needed to provide temperature for reversible heat transfer, while net thermal expansion- compression provides for the net-work out of the cycle.

30 Slide 30 Therefore, … www.kostic.niu.edu... the so called “ waste cooling-heat ” in power cycles (like in thermal power plants) is not waste but very useful heat, necessary for thermal compression of cycling medium (steam-into-condensate, for example), without which it will not be possible to produce mechanical work from heat (i.e., from thermal energy).

31 Slide 31 www.kostic.niu.edu Fig. 8: Significance of the Carnot’s reasoning of reversible cycles is in many ways comparable with the Einstein’s relativity theory in modern times. The Carnot Ratio Equality is much more important than what it appears at first. It is probably the most important equation in Thermodynamics and among the most important equations in natural sciences.

32 Slide 32 Heat Transfer Is Unique and Universal:  Heat transfer is a spontaneous irreversible process where all organized (structural) energies are disorganized or dissipated as thermal energy with irreversible loss of energy potential (from high to low temperature) and overall entropy increase. 2009 January 10-12 © M. Kostic  Thus, heat transfer and thermal energy are unique and universal manifestation of all natural and artificial (man-made) processes, … and thus … are vital for more efficient cooling and heating in new and critical applications, including energy production and utilization, environmental control and cleanup, and bio- medical applications.

33 Slide 33 REVERSIBILITY AND IRREVERSIBILITY: ENERGY TRANSFER AND DISORGANIZATION, RATE AND TIME, AND ENTROPY GENERATION Net-energy transfer is in one direction only, from higher to lower potential (energy-forcing-potential), and the process cannot be reversed. Thus all real processes are irreversible in the direction of decreasing energy-forcing-potential, like pressure and temperature (forced displacement of mass-energy) 2009 January 10-12 © M. Kostic

34 Slide 34 Quasi-equilibrium Process : in limit, energy transfer process with infinitesimal potential difference (still from higher to infinitesimally lower potential, P). Then, if infinitesimal change of potential difference direction is reversed P+dP → P-dP with infinitesimally small external energy, since dP→0, the process will be reversed too, which is characterized with infinitesimal entropy generation, and in limit, without energy degradation (no further energy disorganization) and no entropy generation thus achieving a limiting reversible process. 2009 January 10-12 © M. Kostic

35 Slide 35 Local-Instant & Quasi-Equilibrium: At instant (frozen) time, a locality around a point in space may be considered as ‘instant-local equilibrium’ (including inertial forces) with instantaneous local- properties well-defined, regardless of non- uniformity. Quasi-equilibrium is due to very small energy fluxes due to very small gradients and/or very high impedances, so that changes are infinitely slow, for all practical purposes appearing as equilibrium with virtually net- zero energy exchange. 2009 January 10-12 © M. Kostic

36 Slide 36 REVERSIBILITY –Relativity of Time: Therefore, the changes are ‘fully reversible,’ and along with their rate of change and time, totally irrelevant (no irreversible-permanent change), as if nothing is effectively changing (no permanent-effect to the surroundings or universe) The time is irrelevant as if it does not exist, since it could be reversed or forwarded at will and at no ‘cost’ (no permanent change) and, thus, relativity of time. Real time cannot be reversed, it is a measure of permanent changes, like irreversibility, which is in turn measured by entropy generation. In this regard the time and entropy generation of the universe have to be related. 2009 January 10-12 © M. Kostic

37 Slide 37 The 2 nd Law Definition … Non-equilibrium cannot be spontaneously created. All natural spontaneous, or over-all processes (proceeding by itself and without interaction with the rest of the surroundings) between systems in non-equilibrium have irreversible, forced tendency towards common equilibrium and thus irreversible loss of the original work potential (measure of non-equilibrium), by converting (dissipating) other energy forms into the thermal energy (and degrading the latter to lower temperature) accompanied with increase of entropy (randomized equi-partition of energy per absolute temperature level). www.kostic.niu.edu The 2 nd Law is more than thermo-mechanical (heat-work) energy conversion, but about energy processes in general: Forcing due to non-equilibrium has tendency towards equilibrium.

38 Slide 38 The 2 nd Law “Short” Definition: The useful-energy (non-equilibrium work potential) cannot be created from within equilibrium alone or otherwise, it only can be forcefully transferred between systems (ideally conserved) and irreversibly dissipated towards equilibrium into thermal energy thus generating entropy.The useful-energy (non-equilibrium work potential) cannot be created from within equilibrium alone or otherwise, it only can be forcefully transferred between systems (ideally conserved) and irreversibly dissipated towards equilibrium into thermal energy thus generating entropy. www.kostic.niu.edu The 2 nd Law is more than thermo-mechanical (heat-work) energy conversion, but about energy processes in general: Forcing due to non-equilibrium has tendency towards equilibrium. Force or Forcing is a process of exchanging useful-energy (forced displacement) with net-zero exchange at forced equilibrium.

39 Slide 39 Issues and Confusions … There are many puzzling issues surrounding the Second Law and other concepts in Thermodynamics, including subtle definitions and ambiguous meaning of very fundamental concepts.There are many puzzling issues surrounding the Second Law and other concepts in Thermodynamics, including subtle definitions and ambiguous meaning of very fundamental concepts. Further confusions are produced by attempts to generalize some of those concepts with similar but not the same concepts in other disciplines, like Thermodynamic entropy versus other types of (quasi & statistical) entropies.Further confusions are produced by attempts to generalize some of those concepts with similar but not the same concepts in other disciplines, like Thermodynamic entropy versus other types of (quasi & statistical) entropies. www.kostic.niu.edu Thermodynamic ENTROPY [J/K] is related to thermal energy transfer & generation per absolute temperature; it is a physical concept not a statistical construct (which is only a limited ‘description’ tool) as argued by some.

40 Slide 40 Local Creation of Non-equilibrium … … It should not be confused with local increase/decrease of non-equilibrium and/or ‘organized structures’ on expense of ‘over-all’ non-equilibrium transferred from elsewhere. Non- equilibrium is always “destroyed” by spontaneous and irreversible conversion (dissipation) of other energy forms into the thermal energy, always and everywhere accompanied with entropy generation. (randomized equi-partition of energy per absolute temperature level). www.kostic.niu.edu

41 Slide 41 Definition of Entropy 2009 January 10-12 © M. Kostic "Entropy is ‘an integral measure’ of (random) thermal energy redistribution (stored as property, due to heat transfer or irreversible heat generation) within a system mass and/or space (during system expansion), per absolute temperature level. Entropy is increasing from orderly crystalline structure at zero absolute temperature (zero reference) during reversible heating (entropy transfer) and entropy generation during irreversible energy conversion, i.e. energy degradation or random equi-partition within system material structure and space." (by M. Kostic) "Entropy is ‘an integral measure’ of (random) thermal energy redistribution (stored as property, due to heat transfer or irreversible heat generation) within a system mass and/or space (during system expansion), per absolute temperature level. Entropy is increasing from orderly crystalline structure at zero absolute temperature (zero reference) during reversible heating (entropy transfer) and entropy generation during irreversible energy conversion, i.e. energy degradation or random equi-partition within system material structure and space." (by M. Kostic) Thermodynamic ENTROPY [J/K] is THE specific thermo-physical concept, NOT a statistical concept, i.e., the S=k log (W) is ONLY a SIMPLIFIED/very-limited ‘construct’ not to be extrapolated …

42 Slide 42 Entropy … … entropy of a system for a given state is the same, regardless whether it is reached by reversible heat transfer or irreversible heat or irreversible work transfer (entropy is a state function, while entropy generation is process dependent). Once generated it cannot be destroyed (irreversible change), but transferred only. However, the source entropy will decrease to a smaller extent over higher potential, thus resulting in overall entropy generation for the two interacting systems. 2009 January 10-12 © M. Kostic

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44 Slide 44 … Entropy … We could consider a system internal thermal energy and entropy, as being accumulated from absolute zero level, by disorganization of organized/structural or higher level energy potential with the corresponding entropy generation. Thus entropy as system property is associated with its thermal energy and temperature. (but also space, since mechanical & thermal energies are coupled and equi-partitioned for I.G. (PV=Nk B T): unrestricted expansion is work-potential loss to thermal energy, as is the heat-transfer at finite temperature difference ). Thus entropy as system property is associated with its thermal energy and temperature. (but also space, since mechanical & thermal energies are coupled and equi-partitioned for I.G. (PV=Nk B T): unrestricted expansion is work-potential loss to thermal energy, as is the heat-transfer at finite temperature difference ). 2009 January 10-12 © M. Kostic …thus thermal & mechanical energies are coupled

45 Slide 45 Entropy Summary Thus, entropy transfer is due to reversible heat transfer and could be ether positive or negative (thus entropy is over-all conserved while reversibly transferred). (The Second Law): However, entropy generation is always positive and always due to irreversibility. Thus entropy is Over-ALL increased (The Second Law): 2009 January 10-12 © M. Kostic

46 Slide 46 © M. Kostic “ The Second Law of Thermodynamics is considered one of the central laws of science, engineering and technology. “ The Second Law of Thermodynamics is considered one of the central laws of science, engineering and technology. For over a century it has been assumed to be inviolable by the scientific community. For over a century it has been assumed to be inviolable by the scientific community. Over the last 10-20 years, however, more than two dozen challenges to it have appeared in the physical literature - more than during any other period in its 150-year history.” Second Law Conference: Status and Challenges Second Law Conference: Status and Challenges with Prof. Sheehan in Sun Diego, CA June 2011

47 Slide 47 www.kostic.niu.edu The Second Law Symposium has been a unique gathering of the unorthodox physicist and inventors (to avoid using a stronger word)

48 Slide 48 Cause-and-Effect Phenomena: The forces, due to non-equilibrium of mass- energy in space (non-uniform ‘concentrations’), causing the mass-energy displacement, thus defining the process direction, are manifested by forced tendency of mass-energy transfer in time towards common equilibrium: cause-and-effect force-flux tendency of equi-partition of mass-energy.The forces, due to non-equilibrium of mass- energy in space (non-uniform ‘concentrations’), causing the mass-energy displacement, thus defining the process direction, are manifested by forced tendency of mass-energy transfer in time towards common equilibrium: cause-and-effect force-flux tendency of equi-partition of mass-energy. www.kostic.niu.edu

49 Slide 49 www.kostic.niu.edu Carnot (mistakenly) reasoned that reversibility conserves heat/energy (which is always the case), but he actually ‘proved’ that it conserves non-equilibrium (work-potential), i.e. maximum possible efficiency. Therefore, the non-equilibrium CANNOT be generated.

50 Slide 50 www.kostic.niu.edu There is ‘energy’ (or ‘mass- energy’ as the building block of all existence), subject of the 1st Law of Thermodynamics ; and there is 'useful energy,' or ‘available energy’ i.e., 'work potential' as measure of non-equilibrium, which is the cause-end-effect of forcing energy transfer (all processes) from higher to lower energy density/potential, subject of the 2 nd Law of Thermodynamics.

51 Slide 51 In conclusion … www.kostic.niu.edu … it is only possible to produce work during energy exchange between systems in non-equilibrium, not, for example, within a single thermal reservoir in equilibrium. Actually, the work potential is measure of the systems’ non-equilibrium, thus the work potential could be conserved only in processes if the non-equilibrium is preserved (conserved, i.e. rearranged – cycle work has to be stored eventually), and such ideal processes could be reversed, and thus named reversible processes.

52 Slide 52 In conclusion (2)… www.kostic.niu.edu … When systems come to the forced- equilibrium there is no potential for any process to produce (extract) any work ( no net- forcing !). Therefore, it is impossible to produce (extract) work from a single thermal reservoir in equilibrium: otherwise, non-equilibrium will be spontaneously created (WORK could be produced ONLY on expense of some kind of non-equilibrium, i.e., transferred within a system or transferred from the surrounding systems).

53 Slide 53 In conclusion (3) … www.kostic.niu.edu … It is possible to produce work from thermal energy ONLY in a process between two thermal reservoirs in non-equilibrium (with different temperatures). Consequently, if heat transfer takes place spontaneously at finite temperature difference, without possible reversible Carnot work extraction, the latter work potential will be permanently “lost,” thus irreversibly dissipated into generated thermal energy (thus generating entropy).

54 Slide 54 In conclusion (4) … www.kostic.niu.edu … All real natural processes between systems in non- equilibrium have (forced) tendency towards common equilibrium and thus loss of the original work potential, by converting (“dissipating”) other energy forms into the thermal energy accompanied with entropy generation (randomized equi-partition of energy per absolute temperature level). Due to loss of work potential in a real process, the resulting reduced work cannot reverse back the process to the original non-equilibrium, as is possible with ideal reversible processes.

55 Slide 55 In conclusion (5) … www.kostic.niu.edu … Since non-equilibrium cannot be created or increased spontaneously (by itself and without interaction with the rest of the surroundings) then all reversible processes must be the most and equally efficient (will equally conserve work potential, i.e. conserve non-equilibrium, otherwise will create non-equilibrium by coupling with differently efficient reversible processes, as reasoned by Carnot). The irreversible processes will loose work potential to thermal energy with increase of entropy, thus will be less efficient than corresponding reversible processes. Carnot reasoned that reversibility conserves energy (which is always the case), but he actually ‘proved’ that it conserves non-equilibrium (work-potential), i.e. max possible efficiency.

56 Slide 56 Living and Complex Systems Many creationists (including evolutionists and information scientists) make claims that evolution violates the Second Law. Although biological and some other systems may and do create local non-equilibrium and order (BUT only on expense of elsewhere!), the net change in entropy for all involved systems is positive (due to its unavoidable irreversible local generation) and conforms to the Laws of Nature and the Second Law for non-equilibrium open systems. www.kostic.niu.edu It may appear that the created non-equilibrium structures are self-organizing from nowhere, from within an equilibrium (thus violating the 2nd Law), due to the lack of proper observations and ‘accounting’ of all mass-energy flows, the latter maybe in ‘stealth’ form or undetected rate at our state of technology and comprehension (as the science history has though us many times). It may appear that the created non-equilibrium structures are self-organizing from nowhere, from within an equilibrium (thus violating the 2nd Law), due to the lack of proper observations and ‘accounting’ of all mass-energy flows, the latter maybe in ‘stealth’ form or undetected rate at our state of technology and comprehension (as the science history has though us many times).

57 Slide 57 Crystal ‘self-formation’… www.kostic.niu.edu … and Plant Cells growth It may appear that the created non-equilibrium structures are self-organizing from nowhere, from within an equilibrium (thus violating the 2nd Law), due to the lack of proper ‘observations’ at our state of technology and comprehension (as the science history has though us many times).

58 Slide 58 Nature often defy our intuition Without friction, clock will not work, you could not walk, birds could not fly, and fish could not swim.Without friction, clock will not work, you could not walk, birds could not fly, and fish could not swim. Friction can make the flow go fasterFriction can make the flow go faster Roughening the surface can decrease dragRoughening the surface can decrease drag Adding heat to a flow may lower its temperature, and removing heat from a flow may raise its temperatureAdding heat to a flow may lower its temperature, and removing heat from a flow may raise its temperature Infinitesimally small causes can have large effects (tipping point)Infinitesimally small causes can have large effects (tipping point) Symmetric problems may have non-symmetric solutionsSymmetric problems may have non-symmetric solutions www.kostic.niu.edu

59 Slide 59 www.kostic.niu.edu YES! Miracles are possible ! It may look ‘ perpetuum mobile ’ but miracles are real too … … we could not comprehend energy conservation until 1850s: (mechanical energy was escaping “without being noticed how”) … we may not comprehend now new energy conversions and wrongly believe they are not possible: (“cold fusion” seems impossible for now … ?) …….Let us keep our eyes and our minds ‘open’ ……….. Things and Events are both, MORE but also LESS complex than how they appear and we ‘see’ them -- it is natural simplicity in real complexity

60 Slide 60 www.kostic.niu.edu YES! Miracles are possible ! … but there is NO ideal ‘Things and Events’ … … there are no ideal things, no ideal rigid body, no ideal gas, no perfect elasticity, no adiabatic boundary, no frictionless/reversible process, no perfect equilibrium, not a steady-state process … … there are always processes - energy in transfer or motion, all things/everything ARE energy in motion with unavoidable process irreversibilities, however, in limit, an infinitesimally slow process with negligible irreversibility ‘appears’ as instant reversible equilibrium – thus, everything is relative with regard to different space and time scales ….Let us keep our eyes and our minds ‘open’ ……….. ….Let us keep our eyes and our minds ‘open’ ……….. ‘Things and Events’ are both, MORE but also LESS complex than how they appear and we ‘see’ them: it is natural simplicity in real complexity

61 Slide 61 All processes are transient … All processes are transient (work and heat transfer, and entropy production, in time) and degradive/dissipative, even Eulerian steady-state processes (space-wise) are transient in Lagrangian form (system-wise, from input to output), … but equilibrium processes and even quasi-static (better, quasi-equilibrium) processes are sustainable/reversible. 2009 January 10-12 © M. Kostic The existence in space and transformations in time are manifestations of perpetual mass-energy forced displacement processes: with net-zero mass-energy transfer in equilibrium (equilibrium process) and non-zero mass-energy transfer in non-equilibrium (active process) towards equilibrium.

62 Slide 62 If we are unable to observe … If we are unable to measure something it does not mean it does not exist (it could be sensed or measured with more precise instruments or in a longer time scale, or in similar stronger processes (mc 2 always!, but often not measurable). So called "self-organizing" appear as entropy increasing processes, since we are unable to comprehend or to observe/measure entropy change within or of affecting boundary environment, for such open processes. The miracles are until they are comprehended and understood! 2009 January 10-12 © M. Kostic

63 Slide 63 Simulation and Reality … Entropy is a measure of thermal-energy metaphorical-disorder (with ‘strings’ attached), not a measure of any-form disorder.Entropy is a measure of thermal-energy metaphorical-disorder (with ‘strings’ attached), not a measure of any-form disorder. Einstein is quoted as satted: “Since mathematicians explained ‘Theory of Relativity’, I do not understand it any more.”Einstein is quoted as satted: “Since mathematicians explained ‘Theory of Relativity’, I do not understand it any more.” Similarly, after statisticians explained ‘Entropy’ I do not understand it any more.Similarly, after statisticians explained ‘Entropy’ I do not understand it any more. www.kostic.niu.edu

64 Slide 64 Statistical Interpretation Is Important as Metaphoric Only Again, a statistical interpretation is important as metaphoric only: The sum of the probabilities of possible discrete microstates, p i 's, that could occur during the "random fluctuations" of a given macro-state. The adjective, possible, could occur, consistent random fluctuations (thus thermal), and the holistic of the statement have deep meanings, and could not be evaluated for any real system, but only scaled for the trivial one(s).Again, a statistical interpretation is important as metaphoric only: The sum of the probabilities of possible discrete microstates, p i 's, that could occur during the "random fluctuations" of a given macro-state. The adjective, possible, could occur, consistent random fluctuations (thus thermal), and the holistic of the statement have deep meanings, and could not be evaluated for any real system, but only scaled for the trivial one(s). www.kostic.niu.edu

65 Slide 65 Granted, there are some benefits, BUT … Granted, there are some benefits from simplified statistical descriptions to better understand the randomness of thermal motion and related physical quantities, but the limitations should be stated so the real physics would not be overlooked, or worse discredited. The phenomenological thermodynamics has the supremacy due to logical reasoning based on the fundamental laws and without the regard to the system complex dynamic structure and even more complex interactions. The fundamental laws and physical phenomena could not be caused and governed by mathematical modeling and calculation outcomes as suggested by some, but the other way around. www.kostic.niu.edu

66 Slide 66 www.kostic.niu.edu Thank you! Any Questions ?

67 Slide 67 Appendices Stretching the mind further … www.kostic.niu.edu

68 Slide 68 Entropy Logarithmic Law: dS=C th dT/T then S-S ref =C th *ln(T/T ref ), i.e. proportional to T or thermal motion, or W, number of thermal microstates (depends on thermal motion) that are consistent/correspond to a macrostate.dS=C th dT/T then S-S ref =C th *ln(T/T ref ), i.e. proportional to T or thermal motion, or W, number of thermal microstates (depends on thermal motion) that are consistent/correspond to a macrostate. Many other processes/phenomena are governed by CdX/X and thus Logarithmic Law.Many other processes/phenomena are governed by CdX/X and thus Logarithmic Law. The C th is thermal capacity of any reversible heating process or isochoric thermal capacity Cv otherwiseThe C th is thermal capacity of any reversible heating process or isochoric thermal capacity Cv otherwise www.kostic.niu.edu

69 Slide 69 Entropy and Random Thermal Motion Since entropy is directly related to the random thermal motion of a system micro (atomic and molecular) structure, it is suitable to statistical analysis, particularly of simple system structures, like ideal gases, consisting of completely randomized particle motion in thermal equilibrium, without any other particle interactions, but elastic, random collisions of material point-like particles. For more complex, thus all real systems, the thermal motion and interactions are much more complex, thus the statistical analysis is metaphorical only and cannot be quantitatively reduced to physical entropy, the latter well-defined and measured in laboratory for all substances of practical interest. www.kostic.niu.edu

70 Slide 70 Just because we could scale entropy … Just because we could scale entropy using a statistical description of statistically random thermal motion of simple system particulate structure, the latter related to both, the thermal energy and thermodynamic temperature, thus entropy, it does not mean that entropy is a simple statistical concept and not physical quantity of its own right. Actually, the statistical representation is so simple and so limited, that without knowing the result upfront, the scaling would be impossible but for trivially simple and fully randomized mono-atomic ideal gas structure. www.kostic.niu.edu

71 Slide 71 statistical analysis is ‘going so far’ The interpretation of the statistical analysis is going so far as to forget about the phenomena it is trying to describe, and presenting it as spatial particle arrangement, and or simplified statistics of position and momenta of particles without other realistic interactions. As if entropy is a measure of statistical randomness without reference to thermal energy, or reference to energy in general, both physically inappropriate! www.kostic.niu.edu

72 Slide 72 The real entropy, as defined and measured The real entropy, as defined and measured, is related to the thermal energy and thermodynamic temperature, dS=dQ/T, not others internal energies. The Boltzmann's metaphorical entropy description, S=k*log(W), refers to a logarithmic measure of the number of possible microscopic states (or microstates), W, of a system in thermodynamic equilibrium, consistent with its macroscopic entropy state (thus ‘equivalent’ number of thermal, dynamic microstates). This is really far-fetched qualitative description that transfers all real complexity to W (number of relevant thermal, dynamic microstates) with deep meaning of relevant adjectives: equivalent number of microstates consistent with the well-defined macro-state. thermodynamic equilibrium www.kostic.niu.edu

73 Slide 73 not a number of all possible spatial distributions This is not a number of all possible spatial distributions of micro-particles within the system volume as often graphically depicted. For example, the microstates with all molecules in one half or one quarter of system volume and similar are inappropriate to count, since they are not consistent with the macrostate, nor physically possible to self- force all molecules in one half volume with vacuum in the other half. That would be quite different macrostate with virtually null probability (not equi-probable)! www.kostic.niu.edu

74 Slide 74 Randomness is Statistical The microstate of a very simple, ideal system could be described by the positions and momenta of all the atoms. In principle, all the physical properties of the system are determined by its microstate. The Gibbs or von Neumann quantum or Shanon or other probabilistic entropy descriptions are also statistical as Boltzmann's. positions momenta Actually they all reduce to the latter for fully randomized large system in equilibrium, since the logarithmic probability of all discrete microstates, where, equiprobable p i =1/W, result in the Boltzmann's logarithmic value, i.e.: -Sum(p i *log(p i )=log(W) www.kostic.niu.edu

75 Slide 75 Statistical Interpretation Is Important as Metaphoric Only Again, a statistical interpretation is important as metaphoric only: The sum of the probabilities of possible discrete microstates, p i 's, that could occur during the "random fluctuations" of a given macro-state. The adjective, possible, could occur, consistent random fluctuations (thus thermal), and the holistic of the statement have deep meanings, and could not be evaluated for any real system, but only scaled for the trivial one(s).Again, a statistical interpretation is important as metaphoric only: The sum of the probabilities of possible discrete microstates, p i 's, that could occur during the "random fluctuations" of a given macro-state. The adjective, possible, could occur, consistent random fluctuations (thus thermal), and the holistic of the statement have deep meanings, and could not be evaluated for any real system, but only scaled for the trivial one(s). www.kostic.niu.edu

76 Slide 76 Granted, there are some benefits, BUT … Granted, there are some benefits from simplified statistical descriptions to better understand the randomness of thermal motion and related physical quantities, but the limitations should be stated so the real physics would not be overlooked, or worse discredited. The phenomenological thermodynamics has the supremacy due to logical reasoning based on the fundamental laws and without the regard to the system complex dynamic structure and even more complex interactions. The fundamental laws and physical phenomena could not be caused and governed by mathematical modeling and calculation outcomes as suggested by some, but the other way around. www.kostic.niu.edu

77 Slide 77 U,T & S are subtle and elusive, but … The energy, temperature and entropy are subtle and elusive, but well-defined and precisely measured as physical quantities, and used as such. They should be further refined and explained for what they are and not be misrepresented as something they are not. Any new approach should be correlated with existing knowledge, and limitations clearly and objectively presented. www.kostic.niu.edu

78 Slide 78 www.kostic.niu.edu Entropy thermal displacement propertyJ/K measure of thermal dynamic-disorder relatedto logarithm of number of “all thermal, dynamic-microstates” logarithmic-probability or uncertainty corresponds, or are consistent with thermodynamic macrostate deeply important metaphoric description Entropy, the thermal displacement property, dS=dQ rev /T (or dQ cal /T) with J/K unit, is a measure of thermal dynamic-disorder or thermal randomness, and may be expressed as being related to logarithm of number of “all thermal, dynamic-microstates”, or to their logarithmic-probability or uncertainty, that corresponds, or are consistent with the given thermodynamic macrostate. Note that the meanings of all relevant adjectives are deeply important to reflect reality and as such it has metaphoric description for real systems. Q cal =Q rev +W loss =Q rev +Q diss To repeat again …

79 Slide 79 www.kostic.niu.edu Thank you! Any Questions ?


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