# Thermodynamic Variables of First-Order Entropy Corrected Lovelock-AdS Black Holes : P-V Criticality Analysis

## TL;DR

This paper explores how first-order thermal fluctuations influence the thermodynamics and phase transitions of Lovelock-AdS black holes, revealing that such corrections are essential for criticality and stability.

## Contribution

It introduces the impact of logarithmic entropy corrections on black hole thermodynamics, criticality, and stability, highlighting the necessity of thermal fluctuations for phase transitions.

## Key findings

- Thermal fluctuations decrease thermodynamic potentials.
- Logarithmic corrections are essential for P-V criticality.
- Critical points only exist with thermal fluctuations.

## Abstract

We investigate the effect of thermal fluctuations on the thermodynamics of a Lovelock-AdS black hole. Taking the first order logarithmic correction term in entropy we analyze the thermodynamic potentials like Helmholtz free energy, enthalpy and Gibbs free energy. We find that all the thermodynamic potentials are decreasing functions of correction coefficient $\alpha$. We also examined this correction coefficient tmust be positive by analysing $P-V$ diagram. Further we study the P-V criticality and stability and find that presence of logarithmic correction in it is necessary to have critical points and stable phases. When P-V criticality appears, we calculate the critical volume $V_c$, critical pressure $P_c$ and critical temperature $T_c$ using different equations and show that there is no critical point for this black hole without thermal fluctuations. We also study the geometrothermodynamics of this kind of black holes. The Ricci scalar of the Ruppeiner metric is graphically analysed.