The nonequilibrium Rational Extended Thermodynamics for the fractional exclusion statistics

Abstract We consider the theory of the fractional exclusion statistics (FES) by using both the Maximum Entropy Principle (MEP) and the Entropy Principle (EP) in the context of Rational Extended Thermodynamics (RET) with an arbitrary dimension D of phase space. To this purpose, we develop and apply a general approach for the FES, in both equilibrium and nonequilibrium conditions, by connecting the MEP in a semiclassical local context, with the Boltzmann transport equation (BTE) and with the method of moments in RET. In particular, by using a general expression for the energy dispersion relation, a generalized set of kinetic fields, a generalized set of macroscopic variables, and a generalized set of corresponding Lagrange multipliers: (i) the entropy balance equation is derived, the statistical implications of the theory are discussed, and some thermodynamic properties are explicitly analyzed; (ii) the nonequilibrium theory is explained by determining an explicit linear expansion for both the MEP distribution function and the nonequilibrium Lagrange multipliers; (iii) the construction of an arbitrary set of hydrodynamic equations (HD) in the context of RET is obtained; and (iv) some special cases are explicitly considered.