Cosmological horizon entropy and generalised second law for flat Friedmann Universe

TL;DR

This paper examines the generalized second law of thermodynamics in flat Friedmann universes with different matter contents, analyzing horizon entropy evolution and constraints on temperature during cosmic expansion.

Contribution

It provides an analytical study of horizon and matter entropy evolution in Friedmann universes with radiation or matter and a positive cosmological constant, highlighting GSL constraints.

Findings

GSL constrains the temperature of radiation and matter in Friedmann universes.

Entropy of radiation decreases at late times but increases during early decelerating phases.

Net entropy of radiation or matter can decrease at large times despite overall universe expansion.

Abstract

We discuss the generalized second law (GSL) and the constraints imposed by it for two types of Friedmann universes. The first one is the Friedmann universe with radiation and a positive cosmological constant, and the second one consists of non-relativistic matter and a positive cosmological constant. The time evolution of the event horizon entropy and the entropy of the contents within the horizon are analyses in an analytical way by obtaining the Hubble parameter. It is shown that the GSL constraint the temperature of both the radiation and matter of the Friedmann universe. It is also shown that, even though the net entropy of the radiation (or matter) is decreasing at sufficiently large times as the universe expand, it exhibit an increase during the early times when universe is decelerating. That is the entropy of the radiation within the comoving volume is decreasing only when the universe has got an event horizon.