Heat and work in Markovian quantum master equations: concepts, fluctuation theorems, and computations

TL;DR

This paper reviews the stochastic thermodynamics of Markovian quantum master equations, exploring heat and work definitions through two approaches, and discusses fluctuation theorems with detailed concepts, techniques, and models.

Contribution

It systematically summarizes current understanding of stochastic heat and work in MQMEs using two distinct strategies, including detailed concepts, techniques, and models.

Findings

Two strategies for defining stochastic heat and work in MQMEs are analyzed.

Fluctuation theorems are extended to quantum regimes within these frameworks.

Concrete models illustrate the theoretical results.

Abstract

Markovian quantum master equations (MQMEs) were established nearly half a century ago. They have often been used in the study of irreversible thermodynamics. However, the previous results were mainly concerned about ensemble averages; the stochastic thermodynamics of these systems went unnoticed for a very long time. This situation remained unchanged until a variety of fluctuation theorems in classical and quantum regimes were found in the past two decades. In this paper, we systematically summarize the current understanding on the stochastic heat and work in MQMEs using two distinct strategies. One strategy is to treat the system and its surrounding heat bath as a closed quantum system, to suppose that the evolution of the composite system is unitary under a time-dependent total Hamiltonian and to define the heat and work as the changes in energy by applying two energy measurements scheme to the composite system. The other strategy is to unravel these MQMEs into random quantum jump trajectories (QJTs) and to define the stochastic heat and work along the individual trajectories. Many important physical concepts, mathematical techniques, and fluctuation theorems at different descriptive levels are given in as detailed a manner as possible. We also use concrete models to illustrate these results.