Stochastic thermodynamics and fluctuation theorems for non-linear systems

Abstract We extend stochastic thermodynamics by relaxing the two assumptions that Markovian dynamics must be linear and equilibrium distribution a Boltzmann distribution. show if we require second law to hold when those are relaxed, then it cannot formulated in terms of Shannon entropy. However, thermodynamic consistency is salvaged reformulate generalized entropy; our first result an equation relating precise form non-linear master associated entropy which results consistency. build on this usual trajectory-level definitions quantities appropriate even relaxed. end using these derive extended versions Crooks fluctuation theorem Jarzynski equality apply