# Time dependent dark energy and the thermodynamics of many-body systems

## TL;DR

This paper explores how time-dependent dark energy models influence galaxy clustering thermodynamics, analyzing different equations of state and comparing theoretical predictions with observational data.

## Contribution

It introduces a detailed analysis of thermodynamics in galaxy clustering affected by dynamical dark energy using two specific models, including generalized Chaplygin gas.

## Key findings

- Generalized Chaplygin gas model aligns better with observational data.
- Thermodynamic laws are validated within the galaxy-dark energy system.
- Analytical and numerical results elucidate the impact of dark energy on galaxy correlations.

## Abstract

In this paper, we study the thermodynamics and statistics of the galaxies clustering affected by the dynamical dark energy. We consider two important dark energy models based on time dependent equation of state to evaluate the gravitational partition function. In the first model, we consider barotropic dark energy with time dependent equation of state. However, in the second model, we consider various kinds of Chaplygin gas equation of state which originally introduced by string theory. We calculate, analytically and numerically, the thermodynamic quantities in canonical and grand canonical ensembles. We investigate validity of the second law of thermodynamics for the total system of clustering of galaxies and dynamical dark energy. We finally evaluate the galaxy-galaxy correlation function and compare our model with Peebles's power law and find that the model based on generalized Chaplygin gas may yields to more agreement with observations.