Directed flow in non-adiabatic stochastic pumps
  We analyze the operation of a molecular machine driven by the non-adiabatic variation of external parameters. We derive a formula for the integrated flow from one configuration to another, obtain a "no-pumping theorem" for cyclic processes with thermally activated transitions, and show that in the adiabatic limit the pumped current is given by a geometric expression. 
Saar Rahav, Jordan Horowitz and Christopher Jarzynski