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

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 $β$. The efficiency of an ideal cycle ($η$), consisting of a sequence of isobaric $\to$ isochoric $\to$ isobaric $\to$ isochoric processes, is computed using the exact efficiency formula. It is shown that $η/η_{C}$, with $η_{C}$ the Carnot efficiency (the maximum efficiency available between two fixed temperatures), decreases as we move from the strong coupling regime ($β\to 0$) to the weak coupling domain ($β\to \infty$). 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 $β$ behaves in the same qualitative manner as the spherical black holes.