Nonlocal statistical mechanics: General fractional Liouville equations and their solutions

Nonlocal generalization of classical statistical mechanics is proposed by using the general fractional calculus in the Luchko form. Some basic concepts of nonlocal statistical mechanics in Liouville picture are suggested. Nonlocal analogs of the standard law of probability conservation are suggested in integral and differential forms. Nonlocality is described by the pairs of Sonin kernels that belong to the Luchko set. Examples of solutions of general fractional Liouville equations are proposed for power-law nonlocal-ity in phase space. The introduction gives a brief overview of some approaches to the description of nonlocal statistical mechanics.(c) 2022 Elsevier B.V. All rights reserved.