Microcanonical quantum fluctuation theorems

Abstract

Previously derived expressions for the characteristic function of work performed on a quantum system by a classical external force are generalized to arbitrary initial states of the considered system and to Hamiltonians with degenerate spectra. In the particular case of microcanonical initial states, explicit expressions for the characteristic function and the corresponding probability density of work are formulated. Their classical limit as well as their relations to the corresponding canonical expressions are discussed. A fluctuation theorem is derived that expresses the ratio of probabilities of work for a process and its time reversal to the ratio of densities of states of the microcanonical equilibrium systems with corresponding initial and final Hamiltonians. From this Crooks-type fluctuation theorem a relation between entropies of different systems can be derived which does not involve the time-reversed process. This entropy-from-work theorem provides an experimentally accessible way to measure entropies.

Equalities and Inequalities: Irreversibility and the Second Law of Thermodynamics at the Nanoscale

“…While quantum versions of these results have been studied for some time [124,125,126,127], the past two to three years have seen a surge of interest in this topic [128,129,130,131,132,133,134,135,136,137,138,139,140,141,142]. Quantum mechanics of course involves profound issues of interpretation.…”

Thermodynamic laws in isolated systems

“…We consider such a dogmatic view artificially restrictive, since the very active and successful field of finite-system thermodynamics has contributed substantially to our understanding of physical computation limits [39][40][41], macromolecules [42][43][44][45], and thermodynamic concepts in general [46][47][48][49][50][51][52][53][54][55][56][57][58][59][60] over the past few decades. A scientifically more fruitful approach might be to explore when and why the analytic continuation method 29 produces reasonable predic-tions for heat capacities, pressure, and similar thermodynamic quantities.…”

Irreversible processes without energy dissipation in an isolated Lipkin-Meshkov-Glick model

“…To develop a thermodynamic interpretation, we rely on initial (before the protocol) and intermediate (before the backward process) equilibrium states, which are the key elements of Crook's theorem [2,18]. It has been recently shown that these equilibrium states exist for (almost) any isolated quantum system unitary evolving after (almost) any initial condition, and they coincide with the long-time average, ρ eq = lim T →∞ 1…”

“…It is now well known that microscopic time reversibility entails a number of relations between dissipation in any time-dependent process and the thermodynamic properties of the equilibrium initial and final states [1]. For isolated systems, the work dissipated in a cyclic process is linked to the increase of entropy after the forward part, if the system equilibrates to a microcanonical state after each time-dependent process [2]. But it is also stated that there is a strong connection between irreversibility and information gained or lost by the system, manifested in the physical consequences of the Szilard engine [3] and expressed in the Landauer principle of information erasure [4].…”