The origin of entropy production in spacetime thermodynamics

TL;DR

This paper investigates the origin of entropy production in spacetime thermodynamics, linking it to the ambiguity in approximate Killing vectors, and extends the understanding from Einstein to $f(R)$ gravity theories.

Contribution

It identifies the ambiguity term of approximate Killing vectors as the source of entropy production, generalizing the thermodynamic description to $f(R)$ gravity.

Findings

Ambiguity term causes entropy production in spacetime thermodynamics.

Pure Einstein theory satisfies thermodynamic equilibrium without the ambiguity term.

In $f(R)$ gravity, entropy production includes contributions from shear and other geometric factors.

Abstract

We find that the ambiguity term of approximate Killing vector field is responsible for the entropy production term. Without the ambiguity term, pure Einstein theory and $f(R)$ satisfy the relation of thermodynamic equilibrium. Considering such an ambiguity term of approximate Killing vector field, we can get the entropy production term and the entropy in $f(R)$ with a form defined by Jacobson. In pure Einstein theory, the shear term is the only geometric contribution of entropy production term, while in $f(R)$ it can also contribute. We believe our approach and conclusion can be generalized to other gravity theory.