Work and heat exchanged during sudden quenches of strongly coupled quantum systems

TL;DR

This paper investigates how to define thermodynamic quantities like work and heat in strongly coupled quantum systems during sudden quenches, revealing that only some definitions comply with the second law of thermodynamics.

Contribution

It compares three definitions of internal energy in strongly coupled quantum systems and identifies which satisfy the second law during quenches.

Findings

Only two of the three definitions obey the second law.

The study uses a simple spin model to illustrate the results.

All definitions satisfy the first law by construction.

Abstract

How should one define thermodynamic quantities (internal energy, work, heat, etc.) for quantum systems coupled to their environments strongly? We examine three (classically equivalent) definitions of a quantum system's internal energy under strong-coupling conditions. Each internal-energy definition implies a definition of work and a definition of heat. Our study focuses on quenches, common processes in which the Hamiltonian changes abruptly. In these processes, the first law of thermodynamics holds for each set of definitions by construction. However, we prove that only two sets obey the second law. We illustrate our findings using a simple spin model. Our results guide studies of thermodynamic quantities in strongly coupled quantum systems.