Local effective dynamics of quantum systems: A generalized approach to work and heat

TL;DR

This paper introduces a generalized framework for distinguishing work and heat in quantum systems based on local energy measurements, applicable to arbitrary states and Hamiltonians, including far-from-equilibrium scenarios.

Contribution

It provides a universal method to differentiate work and heat in quantum systems without assumptions on the Hamiltonian or state, encompassing classical and quantum regimes.

Findings

Work corresponds to energy changes not affecting local entropy.

Heat corresponds to entropy-changing energy variations.

Framework applies to non-commuting Hamiltonians and states far from equilibrium.

Abstract

By computing the local energy expectation values with respect to some local measurement basis we show that for any quantum system there are two fundamentally different contributions: changes in energy that do not alter the local von Neumann entropy and changes that do. We identify the former as work and the latter as heat. Since our derivation makes no assumptions on the system Hamiltonian or its state, the result is valid even for states arbitrarily far from equilibrium. Examples are discussed ranging from the classical limit to purely quantum mechanical scenarios, i.e. where the Hamiltonian and the density operator do not commute.