# Effects of Thermal Fluctuations on Non-minimal Regular Magnetic Black Hole

## TL;DR

This paper studies how thermal fluctuations affect the thermodynamics and stability of a non-minimal regular magnetic black hole within Einstein-Yang-Mills theory, revealing increased stability with higher cosmological constant.

## Contribution

It introduces a detailed thermodynamic analysis of non-minimal RBH considering logarithmic entropy corrections and explores stability criteria across different ensembles.

## Key findings

- Non-minimal RBH stability increases with higher cosmological constant.
- Thermodynamic quantities are significantly affected by thermal fluctuations.
- The first law of thermodynamics holds with logarithmic entropy corrections.

## Abstract

We analyze the effects of thermal fluctuations on a regular black hole (RBH) of non-minimal Einstein-Yang-Mill theory with gauge field of magnetic Wu-Yang type and a cosmological constant. We consider the logarithmic corrected entropy in order to analyze the thermal fluctuations corresponding to non-minimal RBH thermodynamics. In this scenario, we develop various important thermodynamical quantities such as entropy, pressure, specific heats, Gibb's free energy and Helmothz free energy. We investigate first law of thermodynamics in the presence of logarithmic corrected entropy and non-minimal RBH. We also discuss the stability of this RBH using various frameworks such as $\gamma$ factor (comprises of ratio of heat capacities), phase transition, grand canonical ensemble and canonical ensemble. It is observed that the non-minimal RBH becomes more globally and locally stable if we increase the value of cosmological constant.