1. Information Thermodynamics on Feedback Process
KIAS Workshop on Quantum Information and Thermodynamics – Nov, 2015, Busan
Information Thermodynamics on Feedback Process
Chulan Kwon
Myongji University
Outline
Feedback process (Maxwell’s demon)
Szilard engine
Feedback by time-varying potential
Cold damping
Summary

2. I. Feedback Process Inside memory device: measurement, erasure
used
Bit (binary digit)
Information
process
empty
erased
Hidden
process
erasure
measurement
system
state
measurement
outcome
memory
state
protocol, external field
feedback
Inside memory device: measurement, erasure
At post-measurement: (Szilard) information engine

3. Maxwell’s demon: violation of thermodynamic second law (1867)
Demon as a memory device: measurement-> information stored
Szilard engine: tractable model (1929)
Shannon entropy:
Landauer’s principle: measurement as thermodynamic process, erasure of memory
(1961)
Erasure
Measurement
Landauer’s principle
Bennet, others: Erasure process can resolve the paradox of demon.
can be negative!

4. Mutual information Measurement
Memory and system as a composite system (T. Sagawa and his group, since 2008)
Mutual information
Measurement
Potential shape change
depending on X
will be used as a measurement error
In the post-measurement process.

5. measurement
Post-measurement
zero correlation
zero mutual information
at pre-measurement
lower entropy
higher mutual information
at measurement
higher entropy
lower mutual information
in post-measurement
Total entropy change of the composite system and the heat bath in post-measurement
Sagawa and Ueda, PRL, 2012
with the aid of
fluctuation theorem
Szilard engine
Exorcism of demon

6. II. Szilard Engine Revisiting: Sagawa & Ueda, PRE, 2012
Step 1: thermal equilibrium
Step 2: insertion of partition and measurement
Step 3: quasi-static expansion according to measurement up to volume fraction
Step 4: removing partition

8. Up to Step 3 (quasi-static)
Maximum extraction of work
In sudden expansion (no work, no heat)

9. Feedback control by time-varying potential
Revisiting: Abreu & Seifert, EPL, 2011; Sagawa & Ueda, 2012
Time-varying potential
Overdamped motion
Step 1: Thermal equilibrium at the beginning

10. Step 2: Measurement
Conditional probability of
outcome for measuring
Joint PDF for :
PDF for
Cond PDF

11. Step 3: Switch the potential
Work done at Step 3

12. Step 4: protocol change in time

13. Total work
Mutual information
Shannon entropy

14. Total entropy change
Quasi-static process
Generalization of the optimal protocol suggested by Parrondo, Horowitz,
Sagawa (Nature Phys, 2015)

15. IV. Cold damping
(with J. Um & H. Park)
Kim & Qian, PRL, 2007; Jourdan et al, Nanotechnology, 2007; Ito & Sano, PRE, 2011 y E
feedback v v
measure

17. Expected for other feedback processes
Repeated with time delay and interval

23. V. Summary
The thermodynamic second law should hold at any instant, not only for cycle.
It was proven for a few examples via the information thermodynamics
based on the mutual information.
The paradox of Maxwell’s demon is resolved.
The feedback process for cold damping is presented.