Thermodynamics without Time

TL;DR

This paper explores the deep connections between thermodynamics, quantum theory, and gravity, emphasizing the relational nature of thermal equilibrium and the emergence of the arrow of time without relying on a temporal background.

Contribution

It reviews covariant thermodynamics and proposes a relational approach to understanding thermal equilibrium in the context of gravity and quantum theory.

Findings

Covariant notion of thermal equilibrium developed

Relational perspective on thermodynamics emphasized

Connections between gravity and thermodynamics analyzed

Abstract

Our fundamental theories, i.e., the quantum theory and general relativity, are invariant under time reversal. Only when we treat system from the point of view of thermodynamics, i.e., averaging between many subsystem components, an arrow of time emerges. The relation between thermodynamic and the quantum theory has been fertile, deeply explored and still a source of new investigations. The relation between the quantum theory and gravity, while it has not yet brought an established theory of quantum gravity, has certainly sparkled in depth analysis and tentative new theories. On the other hand, the connection between gravity and thermodynamics is less investigated and more puzzling. I review a selection of results in covariant thermodynamics, such as the construction of a covariant notion of thermal equilibrium by considering tripartite systems. I discuss how such construction requires a relational take on thermodynamics, similarly of what happens in the quantum theory and in gravity