On the Einstein–Smoluchowski relation in the framework of generalized statistical mechanics

L.R. Evangelista, E.K. Lenzi, G. Barbero and A.M. Scarfone

Physica A: Statistical Mechanics and its Applications, 2024, vol. 635, issue C

Abstract: Anomalous statistical distributions that exhibit asymptotic behavior different from the exponential Boltzmann–Gibbs tail are typical of complex systems constrained by long-range interactions or time-persistent memory effects at the stationary non-equilibrium or meta-equilibrium. In this framework, a nonlinear Smoluchowski equation, which models the system’s time evolution towards its steady state, is obtained using the gradient flow method based on a free-energy potential related to a given generalized entropic form. Comparison of the stationary distribution resulting from the maximization of entropy for a canonical ensemble with the steady state distribution resulting from the Smoluchowski equation gives an Einstein-Smoluchowski-like relation. Despite this relationship between the mobility of particle μ and the diffusion coefficient D retains its original expression: μ=βD, appropriate considerations, physically motivated, force us an interpretation of the parameter β different from the traditional meaning of inverse temperature.

Keywords: Einstein–Smoluchowski relation; Maximal entropy principle; Zeroth principle of thermodynamics; Physical temperature (search for similar items in EconPapers)
Date: 2024
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Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:635:y:2024:i:c:s0378437123010464

DOI: 10.1016/j.physa.2023.129491

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