The FRW Universe as a van der Waals-like Thermodynamic Heat Engine

TL;DR

This paper models the FRW universe as a thermodynamic heat engine using van der Waals-like equations, analyzing cycle efficiencies and confirming they adhere to classical thermodynamic limits.

Contribution

It introduces a novel approach to treat the FRW universe as a heat engine based on its van der Waals-like thermodynamics, exploring cycle efficiencies.

Findings

Rectangular cycle efficiency remains below unity.

Carnot cycle efficiency sets the thermodynamic upper limit.

FRW universe behaves consistently with classical thermodynamics.

Abstract

It is well known that the Friedmann-Robertson-Walker (FRW) universe is a dynamical spacetime, and it has thermodynamics embodied on the apparent horizon. Notably, it also possesses a van der Waals-like equation of state, enabling us to consider thermodynamic cycles and explore the potential of the FRW universe as a heat engine. In this paper, we investigate two types of cycle--the Carnot cycle and the rectangular cycle--based on the phase diagram derived from the equation of state, to study the heat engine characteristics of the FRW universe. Furthermore, we calculate the work done and assess the corresponding efficiencies, illustrating the efficiency diagram for the FRW universe's heat engine. We observe that the efficiency of the rectangular cycle consistently remains below unity and never exceeds the Carnot efficiency--the thermodynamic upper limit. This finding is in alignment with the traditional thermodynamic principles that govern heat engines.