# Thermodynamic constraints on matter creation models

## TL;DR

This paper uses thermodynamic principles, particularly entropy conditions, to analyze and constrain matter creation models in cosmology, focusing on the evolution of entropy across different eras of the universe.

## Contribution

It introduces a thermodynamic framework based on entropy derivatives to estimate parameter intervals in Creation Cold Dark Matter models.

## Key findings

- Entropy conditions restrict model parameters.
- Thermodynamic equilibrium is achieved in a final de Sitter era.
- Total entropy includes horizon, matter, and radiation contributions.

## Abstract

Entropy is a fundamental concept from Thermodynamics and it can be used to study models on context of Creation Cold Dark Matter (CCDM). From conditions on the first ($\dot{S}\geq0$)\footnote{Throughout the present work we will use dots to indicate time derivatives and dashes to indicate derivatives with respect to scale factor.} and second order ($\ddot{S}<0$) time derivatives of total entropy in the initial expansion of Sitter through the radiation and matter eras until the end of Sitter expansion, it is possible to estimate the intervals of parameters. The total entropy ($S_{t}$) is calculated as sum of the entropy at all eras ($S_{\gamma}$ and $S_{m}$) plus the entropy of the event horizon ($S_h$). This term derives from the Holographic Principle where it suggests that all information is contained on the observable horizon. The main feature of this method for these models are that thermodynamic equilibrium is reached in a final de Sitter era. Total entropy of the universe is calculated with three terms: apparent horizon ($S_{h}$), entropy of matter ($S_{m}$) and entropy of radiation ($S_{\gamma}$). This analysis allows to estimate intervals of parameters of CCDM models.