A unified approach to the derivation of work theorems for equilibrium and steady-state, classical and quantum Hamiltonian systems

TL;DR

This paper introduces a unified method for deriving work theorems applicable to both classical and quantum Hamiltonian systems in equilibrium and steady states, aiding in the calculation of thermodynamic quantities.

Contribution

It provides a simple, unified approach to derive work theorems for classical and quantum systems, including new equalities for nonequilibrium conditions.

Findings

Rederived known work equalities for classical and quantum systems.

Derived new equalities applicable to nonequilibrium systems.

Facilitates determination of partition functions and free energies.

Abstract

We present a unified and simple method for deriving work theorems for classical and quantum Hamiltonian systems, both under equilibrium conditions and in a steady state. Throughout the paper, we adopt the partitioning of the total Hamiltonian into the system part, the bath part, and their coupling. We rederive many equalities which are available in the literature and obtain a number of new equalities for nonequilibrium classical and quantum systems. Our results can be useful for determining partition functions and (generalized) free energies through simulations and/or measurements performed on nonequilibrium systems.