Peculiar thermal states in the first-order thermodynamics of gravity

TL;DR

This paper explores unusual thermal states in first-order thermodynamics of various scalar-tensor gravity theories, revealing non-standard temperature states and extending the formalism to Nordström gravity.

Contribution

It identifies zero-temperature equilibrium states in alternative gravity theories and extends the thermodynamic formalism to Nordström gravity, highlighting novel thermal properties.

Findings

Existence of zero-temperature states in non-Einstein gravity theories

Negative temperature state in Nordström gravity

Extension of thermodynamic formalism to scalar-only gravity

Abstract

In the context of the recently proposed first-order thermodynamics of scalar-tensor gravity, we discuss the possibility of zero-temperature states of equilibrium other than Einstein gravity, including pathological Brans-Dicke theory, Palatini $f(R)$ gravity, and cuscuton gravity, all with non-dynamical scalar fields. The formalism is extended to Nordstr\"om gravity, which contains only a scalar degree of freedom and has negative temperature relative to general relativity.