Single Particle Stochastic Heat Engine
  We have performed an extensive analysis of a single particle stochastic heat engine constructed by manipulating a Brownian particle in a time dependent harmonic potential. The cycle consists of two isothermal steps at different temperatures and two adiabatic steps similar to that of a Carnot engine. The engine shows qualitative differences in inertial and overdamped regimes. All the thermodynamic quantities, including efficiency, exhibit strong fluctuations in a time periodic steady state. The fluctuations of stochastic efficiency dominate over the mean values even in the quasistatic regime. Interestingly, our system acts as an engine provided the temperature difference between the two reservoirs is greater than a finite critical value which in turn depends on the cycle time and other system parameters. This is supported by our analytical results carried out in the quasistatic regime. Our system works more reliably as an engine for large cycle times. By studying various model systems we observe that the operational characteristics are model dependent. Our results clearly rules out any universal relation between efficiency at maximum power and temperature of the baths. We have also verified fluctuation relations for heat engines in time periodic steady state. 
Shubhashis Rana, P. S. Pal, Arnab Saha and A. M. Jayannavar
cond-mat.stat-mech