Generalized transport equation with nonlocality of space–time. Zubarev’s NSO method

P.P. Kostrobij, B.M. Markovych, O.V. Viznovych and M.V. Tokarchuk

Physica A: Statistical Mechanics and its Applications, 2019, vol. 514, issue C, 63-70

Abstract: We presented a general approach for obtaining the generalized transport equations with fractional derivatives by using the Liouville equation with fractional derivatives for a system of classical particles and Zubarev’s nonequilibrium statistical operator (NSO) method within Renyi statistics. New non-Markovian diffusion equations for particles in spatially heterogeneous environment with fractal structure and a generalized Cattaneo-type diffusion equation with taking into account nonlocality of space–time are obtained. Different models of frequency-dependent memory functions, which lead to known diffusion equations with nonlocality of space–time and their generalizations are studied.

Keywords: Cattaneo equation; Maxwell–Cattaneo diffusion equation; Renyi statistics; Nonequilibrium statistical operator (search for similar items in EconPapers)
Date: 2019
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Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:514:y:2019:i:c:p:63-70

DOI: 10.1016/j.physa.2018.09.051

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