Scalar field as a perfect fluid: thermodynamics of minimally coupled scalars and Einstein frame scalar-tensor gravity

TL;DR

This paper refines the analogy between minimally coupled scalar fields and perfect fluids, improving the thermodynamic understanding of scalar-tensor gravity and enabling the Einstein frame formulation.

Contribution

It corrects previous identifications of thermodynamic quantities and advances the thermodynamic interpretation of scalar-tensor theories in the Einstein frame.

Findings

Corrected the effective temperature and chemical potential identifications.

Enabled the first consistent thermodynamic formulation in the Einstein frame.

Provided insights for further development of the scalar-fluid analogy.

Abstract

We revisit the analogy between a minimally coupled scalar field in general relativity and a perfect fluid, correcting previous identifications of effective temperature and chemical potential. This provides a useful complementary picture for the first-order thermodynamics of scalar-tensor gravity, paving the way for the Einstein frame formulation (which eluded previous attempts) and raises interesting questions to further develop the analogy.