Thermodynamics of the FLRW apparent horizon

TL;DR

This paper explores the thermodynamic properties of the apparent horizon in FLRW spacetime, deriving fundamental equations and analyzing conditions under which it behaves as a thermodynamic system, especially considering the effects of a cosmological constant.

Contribution

It provides a detailed analysis of the thermodynamic interpretation of the FLRW apparent horizon, including derivation of fundamental equations and conditions for thermodynamic behavior.

Findings

Thermodynamic interpretation is valid only under specific conditions.

The presence of a cosmological constant affects the thermodynamic properties.

The analogy between gravity and thermodynamics is not universally applicable.

Abstract

To investigate the relationship between gravity and thermodynamics in the case of dynamic systems, we interpret the apparent horizon of the Friedmann-Lema\^itre-Robertson-Walker (FLRW) spacetime as a thermodynamic system. We derive the corresponding fundamental equation in the entropy representation and explore the consequences of demanding the fulfillment of the classical laws of thermodynamics. We investigate in detail the case of an FLRW spacetime with and without cosmological constant. We show that the interpretation of the apparent horizon as a thermodynamic system is possible only under certain conditions because the analogy is not always valid for all the values of the parameters entering the dynamics of the horizon and certainly not for its entire evolution.