Quantum thermodynamics with multiple conserved quantities

TL;DR

This paper explores quantum thermodynamics with multiple conserved quantities, emphasizing the role of the generalized Gibbs ensemble, addressing non-commuting observables, and discussing thermodynamic trade-offs and future challenges.

Contribution

It introduces a comprehensive framework for quantum thermodynamics with multiple conserved quantities, including derivations from micro-canonical ensembles and resource theories, and addresses non-commuting observables.

Findings

Generalized Gibbs ensemble characterizes systems with multiple conserved quantities.

Non-commuting observables can be managed through specific theoretical approaches.

Thermodynamic costs can be redistributed among different observables.

Abstract

In this chapter we address the topic of quantum thermodynamics in the presence of additional observables beyond the energy of the system. In particular we discuss the special role that the generalized Gibbs ensemble plays in this theory, and derive this state from the perspectives of a micro-canonical ensemble, dynamical typicality and a resource-theory formulation. A notable obstacle occurs when some of the observables do not commute, and so it is impossible for the observables to simultaneously take on sharp microscopic values. We show how this can be circumvented, discuss information-theoretic aspects of the setting, and explain how thermodynamic costs can be traded between the different observables. Finally, we discuss open problems and future directions for the topic.