  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.
