Quantum and classical fluctuation theorems from a decoherent histories, open-system analysis

TL;DR

This paper provides a first-principles quantum analysis of fluctuation theorems for open systems, demonstrating their validity at high temperatures and exploring their limits at low temperatures using decoherent histories and Langevin dynamics.

Contribution

It introduces a micro-physics based open-system framework to derive and validate fluctuation theorems for quantum systems interacting with environments.

Findings

Validates fluctuation theorems at high temperatures

Provides formal expressions for work and free energy differences

Identifies parameter regimes where the theorems may not hold

Abstract

In this paper we present a first-principles analysis of the nonequilibrium work distribution and the free energy difference of a quantum system interacting with a general environment (with arbitrary spectral density and for all temperatures) based on a well-understood micro-physics (quantum Brownian motion) model under the conditions stipulated by the Jarzynski equality [C. Jarzynski, Phys. Rev. Lett. 78, 2690 (1997)] and Crooks' fluctuation theorem [G. E. Crooks, Phys. Rev. E 60, 2721 (1999)] (in short FTs). We use the decoherent history conceptual framework to explain how the notion of trajectories in a quantum system can be made viable and use the environment-induced decoherence scheme to assess the strength of noise which could provide sufficient decoherence to warrant the use of trajectories to define work in open quantum systems. From the solutions to the Langevin equation governing the stochastic dynamics of such systems we were able to produce formal expressions for these quantities entering in the FTs, and from them prove explicitly the validity of the FTs at the high temperature limit. At low temperatures our general results would enable one to identify the range of parameters where FTs may not hold or need be expressed differently. We explain the relation between classical and quantum FTs and the advantage of this micro-physics open-system approach over the phenomenological modeling and energy-level calculations for substitute closed quantum systems.