Fluctuations of work from quantum subensembles: The case against quantum work-fluctuation theorems

A. E. Allahverdyan, Th. M. Nieuwenhuizen
2005 Physical Review E  
We study how Thomson's formulation of the second law of thermodynamics ͑no work is extracted from an equilibrium ensemble by a cyclic process͒ emerges in the quantum situation through the averaging over fluctuations of work. The latter concept is carefully defined for an ensemble of quantum systems, the members of which interact with macroscopic sources of work. The approach is based on splitting a mixed quantum ensemble into pure subensembles, which according to quantum mechanics are maximally
more » ... complete and irreducible. The splitting is done by filtering the outcomes of a measurement process. The approach is corroborated by comparing to relevant experiments in quantum optics. A critical review is given of two other approaches to fluctuations of work proposed in the literature. It is shown that in contrast to those, the present definition ͑i͒ is consistent with the physical meaning of the concept of work as mechanical energy lost by the macroscopic sources, or, equivalently, as the average energy acquired by the ensemble; ͑ii͒ applies to an arbitrary nonequilibrium state. There is no direct generalization of the classical work-fluctuation theorem to the proper quantum domain. This implies nonclassical scenarios for the emergence of the second law. 1 It was thus rather surprising to see recent claims on "violations of the second law" ͓10͔ or "transient violations of the second law" ͓11͔ due to fluctuations; see in this context our comment ͓12͔. 2 These features of work are in contrast to those of entropy, whose meaning is too closely tied to equilibrium states of macroscopic bodies. PHYSICAL REVIEW E 71, 066102 ͑2005͒ those definitions; see, e.g., ͓16,18,27,28,30-32͔. 6 As with any exchange process, this is operationally characterized by measurements at two different times. 7 Normally this averaging is done either by letting many identically prepared systems interact with the work source, or by operating with a single system but repreparing its state after each interaction period. Both these ways are feasible and are realized experimentally; see Sec. III G for more details. A. E. ALLAHVERDYAN AND Th. M. NIEUWENHUIZEN PHYSICAL REVIEW E 71, 066102 ͑2005͒ 066102-2 FLUCTUATIONS OF WORK FROM QUANTUM... PHYSICAL REVIEW E 71, 066102 ͑2005͒ 066102-3 A. E. ALLAHVERDYAN AND Th. M. NIEUWENHUIZEN PHYSICAL REVIEW E 71, 066102 ͑2005͒ 066102-4 9 Due to weak coupling to the bath, the energy costs for switching the interaction on and off become negligible. This holds in both the quantum and the classical situations ͓14,15͔. 10 Note that this time dependence is in the Schrödinger representation. To avoid confusion we do not deal with the implicit Heisenberg representation. A. E. ALLAHVERDYAN AND Th. M. NIEUWENHUIZEN PHYSICAL REVIEW E 71, 066102 ͑2005͒ 066102-6
doi:10.1103/physreve.71.066102 pmid:16089815 fatcat:b5kpy5utyzg3pbjr6in5tegmue