In this study, we consider the non-Markovian dynamics of the generic non-equilibrium kinetic process. We summarize the generalized master equation, the continuous and discrete forms of the time-fractional diffusion equation. Using path integral formulation, we generalized the solutions of the Markovian system to the non-Markovian for the non-equilibrium kinetic processes. Then, we obtain the time-fractional kinetic equation for the non-equilibrium systems in terms of free energy. Finally, we introduce a time-fractional equation to analyse time evolution of the open probability for the deformed voltage-gated ion-channel system as an example.
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| http://www.ncbi.nlm.nih.gov/pmc/articles/PMC8523695 | PMC |
| http://dx.doi.org/10.1038/s41598-021-00135-7 | DOI Listing |
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