Thermodynamic resource theories, non-commutativity and maximum entropy principles

TL;DR

This paper explores thermodynamics with multiple conserved quantities, highlighting differences between maximum entropy and passivity approaches, and discusses limitations in current resource theories related to non-commutativity.

Contribution

It generalizes the Landauer principle for multiple conserved quantities and compares maximum entropy and passivity methods in the context of non-commuting observables.

Findings

Tradeoffs in erasure costs for different conserved quantities

Differences between maximum entropy and passivity approaches with multiple observables

Current resource theories may not fully capture non-commutative thermodynamic aspects

Abstract

We discuss some features of thermodynamics in the presence of multiple conserved quantities. We prove a generalisation of Landauer principle illustrating tradeoffs between the erasure costs paid in different "currencies". We then show how the maximum entropy and complete passivity approaches give different answers in the presence of multiple observables. We discuss how this seems to prevent current resource theories from fully capturing thermodynamic aspects of non-commutativity.