Holographic Heat Engines Coupled with Logarithmic $U(1)$ Gauge Theory

TL;DR

This paper investigates the efficiency of holographic heat engines using charged AdS black holes in logarithmic nonlinear $U(1)$ gauge theory, revealing how efficiency varies with the non-linearity parameter and coupling regimes.

Contribution

It introduces a new class of holographic heat engines based on logarithmic $U(1)$ AdS black holes and analyzes their efficiency across different coupling strengths and geometries.

Findings

Efficiency decreases from strong to weak coupling regimes.

Analytic efficiency relations are derived for various temperature limits.

Efficiency behavior is similar across spherical, planar, and hyperbolic black holes.

Abstract

In this paper we study a new class of holographic heat engines via charged AdS black hole solutions of Einstein gravity coupled with logarithmic nonlinear $U(1)$ gauge theory. So, Logarithmic $U(1)$ AdS black holes with a horizon of positive, zero and negative constant curvatures are considered as a working substance of a holographic heat engine and the corrections to the usual Maxwell field are controlled by non-linearity parameter $\beta$. The efficiency of an ideal cycle ($\eta$), consisting of a sequence of isobaric $\to$ isochoric $\to$ isobaric $\to$ isochoric processes, is computed using the exact efficiency formula. It is shown that $\eta/\eta_{C}$, with $\eta_{C}$ the Carnot efficiency (the maximum efficiency available between two fixed temperatures), decreases as we move from the strong coupling regime ($\beta \to 0$) to the weak coupling domain ($\beta \to \infty$). We also obtain analytic relations for the efficiency in the weak and strong coupling regimes in both low and high temperature limits. The efficiency for planar and hyperbolic logarithmic $U(1)$ AdS black holes is computed and it is observed that efficiency versus $\beta$ behaves in the same qualitative manner as the spherical black holes.