Font Size: 

We consider an out-of-equilibrium lattice model consisting of 2D discrete rotators, in contact with heath reservoirs at different temperatures.  The equilibrium counterpart of such model, the clock-model, exhibits three phases, a low-temperature ordered phase, a quasi-liquid phase, and a high temperature disordered phase, with two corresponding phase transitions, the second one being a Berezinskii--Kosterlitz--Thouless transition characterized by weak singularities.
In the out-of-equilibrium model the simultaneous  breaking of spatial and thermal equilibrium give rise to directed rotation of the spin variables describing the direction of the rotators. In this regime the system behaves as a thermal machine converting heat currents into motion.
We introduce and study a dynamical response function and we show that the the optimal operational regime for such a thermal machine occurs when the out-of-equilibrium disturbance is applied on the  critical system at the boundary between the first two phases, namely where the system is mostly susceptible to external thermodynamic forces. Perturbing the system at the  Berezinskii--Kosterlitz--Thouless  transition does not give raise to any relevant  motor effect.  We thus argue that critical fluctuations in system of interacting motors can be exploited to enhance the machine overall dynamic and thermodynamic performances.