Stochastic thermodynamics and fluctuation theorems for non-linear systems

Abstract

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

References in corpus (9)

• Thermodynamic uncertainty relation for biomolecular processes
• Stochastic thermodynamics of chemical reaction networks
• Maximum Caliber: a general variational principle for dynamical systems
• Finite Bath Fluctuation Theorem
• Conceptual Inadequacy of the Shore and Johnson Axioms for Wide Classes of Complex Systems
• Tsallis Ensemble as an Exact Orthode
• Consistency of the structure of Legendre transform in thermodynamics with the Kolmogorov-Nagumo average
• The world according to Renyi: Thermodynamics of multifractal systems
• Markovian master equation for nonlinear systems

Cited by in corpus (3)

• Thermodynamics of exponential Kolmogorov-Nagumo averages
• Generalized free energy and excess/housekeeping decomposition in nonequilibrium systems: from large deviations to thermodynamic speed limits
• Generalized replicator dynamics based on mean-field pairwise comparison dynamic