A Resource Theory for Work and Heat

TL;DR

This paper develops a new quantum resource theory for thermodynamics that does not assume an infinite thermal reservoir, classifying states by entropy and energy, and providing insights into heat engine efficiency and state conversion.

Contribution

It introduces a resource theory of quantum thermodynamics without a background temperature, unifying work and heat, and characterizing states via an energy-entropy diagram.

Findings

All quantum states are classified by entropy and average energy.

Thermodynamics is represented in a two-dimensional energy-entropy diagram.

Resource questions like engine efficiency can be analyzed from the diagram.

Abstract

Several recent results on thermodynamics have been obtained using the tools of quantum information theory and resource theories. So far, the resource theories utilised to describe thermodynamics have assumed the existence of an infinite thermal reservoir, by declaring that thermal states at some background temperature come for free. Here, we propose a resource theory of quantum thermodynamics without a background temperature, so that no states at all come for free. We apply this resource theory to the case of many non-interacting systems, and show that all quantum states are classified by their entropy and average energy, even arbitrarily far away from equilibrium. This implies that thermodynamics takes place in a two-dimensional convex set that we call the energy-entropy diagram. The answers to many resource-theoretic questions about thermodynamics can be read off from this diagram, such as the efficiency of a heat engine consisting of finite reservoirs, or the rate of conversion between two states. This allows us to consider a resource theory which puts work and heat on an equal footing, and serves as a model for other resource theories.