Time-fractional kinetic equation for the non-equilibrium processes

Abstract

In this study, we analytically formulated the path integral representation of the conditional probabilities for the non-equilibrium and non-Markovian kinetic processes in terms of the free energy of the thermodynamic system. We analytically obtain the time-fractional kinetic equations for theseprocesses. Additionally, we give an example to discuss the time-fractional kinetic equation for theopen probability depend on the Helmholtz free energy of the non-equilibrium and non-Markovianchannel system.