Abstract
The non-linear Fokker-Planck equation or Kolmogorov forward equation is currently successfully applied for deep analysis of irreversibility and it gives an excellent approximation near the free energy minimum, just as Boltzmann’s definition of entropy follows from finding the maximum entropy state. A connection to Fokker-Planck dynamics and the free energy functional is presented and discussed—this approach has been particularly successful to deal with metastability. We focus our attention on investigating and discussing the fundamental role of dissipation analysis in metastable systems. The major novelty of our approach is that the obtained results enable us to reveal an appealing, and previously unexplored relationship between Fokker-Planck equation and the associated free energy functional. Namely, we point out that the dynamics may be regarded as a gradient flux, or a steepest descent, for the free energy.
Highlights
Stochastic differential equations are used to model many complex systems in physics, chemistry, biology, economics, and engineering, including population dynamics, protein kinetics, turbulence, etc.In this context, the Fokker-Planck equation represents the probability density for the position or the velocity of a particle which motion is well described by Langevin’s equation and how a collection of their initial physical data evolves with time
The ATP diffusion process inside the cell is a diffusion process and it can be worthy studied by Fokker-Planck equation and entropy generation approach as we show in the paragraph
In [17] it is said that probability of violation of the Second Law of thermodynamics becomes exponentially small as τ increases, with τ the time duration of the physical process
Summary
Stochastic differential equations are used to model many complex systems in physics, chemistry, biology, economics, and engineering, including population dynamics, protein kinetics, turbulence, etc. The solution of the Fokker-Planck equation is a powerful tool that allows one to follow at each instant the direction of a gradient flux of the associated free energy functional by a discrete time formulation, based on the Wasserstein metric [1]. By this approach metastability and hysteresis in physical systems could be treated in a satisfactory way [1,2,3,4]. In this paper we apply Fokker-Plank equation to dissipation phenomena, with particular regards to the entropy generation and we come to a consistent statistical description
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