Entropy Production in Mesoscopic Stochastic Thermodynamics:   Nonequilibrium Kinetic Cycles Driven by Chemical Potentials, Temperatures,   and Mechanical Forces
  Nonequilibrium thermodynamics (NET) investigates processes in systems out of global equilibrium. On a mesoscopic level, it provides a statistical dynamic description of various complex phenomena such as chemical reactions, ion transport, diffusion, thermochemical, thermomechanical and mechanochemical fluxes. In the present review, we introduce a mesoscopic stochastic formulation of NET by analyzing entropy production in several simple examples. The fundamental role of nonequilibrium steady-state cycle kinetics is emphasized. The statistical mechanics of Onsager's reciprocal relations in this context is elucidated. Chemomechanical, thermomechanical, and enzyme-catalyzed thermochemical energy transduction processes are discussed. It is argued that mesoscopic stochastic NET provides a rigorous mathematical basis of fundamental concepts needed for understanding complex processes in chemistry, physics and biology, and which is also relevant for nanoscale technological advances. 
Hong Qian, Signe Kjelstrup, Anatoly B. Kolomeisky and Dick Bedeaux
cond-mat.stat-mech