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

Author

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

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.

Suggested Citation

  • Evangelista, L.R. & Lenzi, E.K. & Barbero, G. & Scarfone, A.M., 2024. "On the Einstein–Smoluchowski relation in the framework of generalized statistical mechanics," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 635(C).
    • Handle: RePEc:eee:phsmap:v:635:y:2024:i:c:s0378437123010464
    DOI: 10.1016/j.physa.2023.129491
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