Refined Second Law of Thermodynamics for fast random processes
  We establish a refined version of the Second Law of Thermodynamics for Langevin stochastic processes describing mesoscopic systems driven by conservative or non-conservative forces and interacting with thermal noise. The refinement is based on the Monge-Kantorovich optimal mass transport. General discussion is illustrated by numerical analysis of a model for micron-size particle manipulated by optical tweezers. 
Erik Aurell, Krzysztof Gaw\c{e}dzki, Carlos Mej\'ia-Monasterio, Roya   Mohayaee, Paolo Muratore-Ginanneschi
cond-mat.stat-mech