1. CONDENSATION OF FLUCTUATIONS IN A TEMPERATURE QUENCH Marco Zannetti - U Salerno in collaboration with Federico Corberi - U Salerno Giuseppe Gonnella - U Bari Antonio Piscitelli - U Napoli

2. temperature quench study of fluctuations during relaxation energy heat

3. temperature quench Brownian Oscillator Gaussian Model : collection of independent oscillators condensation of fluctuations

4. temperature quench Brownian Oscillator Gaussian Model Large – N Model: mean field of interacting system no equilibration!

5. Oscillator

7. effective temperature J.R.Gomez-Solano, A.Petrosyan, S.Ciliberto – PRL 106, 200602 (2011)

8. effective temperature

9. Energy fluctuations 0t

10. Heat fluctuations q < 0 heat released q > 0 heat absorbed

12. fluctuation relation

14. collection of brownian oscillators GAUSSIAN MODEL

15. Temperature Quench

16. spectrum of effective temperatures

17. Fluctuations of extensive quantities: Energy

19. partition function in the biased ensemble

20. Fluctuations of extensive quantities: Energy biased free energy

21. Fluctuations of extensive quantities: Energy large V saddle point ẑ

22. fluctuations in the gaussian model average properties in the biased ensemble condensation spherical model BEC

23. condensation

25. hottest mode

26. condensation

28. finite contribution from the zero mode

29. phase diagram condensed normal

30. phase diagram condensed normal

31. Fluctuations of extensive quantities: Heat

33. most releasing mode saddle point ẑ

35. phase diagram condensed normal

36. N-VECTOR MODEL

38. Large N limit self-average

39. Large N limit self-average

40. Large N limit self-average

41. Temperature Quench

43. unstable modes

44. effective temperatures

47. system permanently out of equilibrium «apparent» equilibrium

48. energy fluctuations

49. normal fluctuations

51. hottest mode coldest mode

52. condensation of negative energy fluctuations due to unstable modes

53. phase diagram normal condensed normal LARGE-N condensed normal GAUSSIAN

54. J. Phys. A: Math. Theor. 46, 042001 (2013) condensation

55. conclusions and outlook Fluctuations of energy and heat after a temperature quench non trivial even in trivial non interacting systems Condensation of fluctuations is related to the duality fluctuations in unbiased ensemble ↔ average properties in biased ensemble Effective temperature key quantity – relation with effective temperature from FDR Mean field qualitatively different from real system (energy unbounded below) - go beyond mean field