Entropy-Based Formulation of Thermodynamics in Arbitrary Quantum Evolution

TL;DR

This paper introduces a universal entropy-based framework for analyzing thermodynamics in arbitrary quantum evolutions, separating heat and work contributions and describing their geometric and dynamical properties.

Contribution

It provides a novel, unambiguous method to decompose energy changes into heat and work for open quantum systems, with a new expression for entropy production independent of the environment.

Findings

Decomposition of energy change into heat and work for quantum systems.

Development of a universal dynamical equation describing quantum trajectories.

Illustration of the framework with three example systems.

Abstract

Given the evolution of an arbitrary open quantum system, we formulate a general and unambiguous method to separate the internal energy change of the system into an entropy-related contribution and a part causing no entropy change, identified as heat and work, respectively. We also demonstrate that heat and work admit geometric and dynamical descriptions by developing a universal dynamical equation for the given trajectory of the system. The dissipative and coherent parts of this equation contribute exclusively to heat and work, where the specific role of a work contribution from a counterdiabatic drive is underlined. Next we define an expression for the irreversible entropy production of the system which does not have explicit dependence on the properties of the ambient environment; rather, it depends on a set of the system's observables excluding its Hamiltonian and is independent of internal energy change. We illustrate our results with three examples.