Derivation of hydrodynamic and quasi-hydrodynamic equations for transport systems based on statistics of Tsallis

Applying the formalism of the Tsallis nonadditive statistical mechanics, a derivation of hydrodynamic and quasi-hydrodynamic equations is considered based on the generalized BGK kinetic equation. In particular, those equations are intended for construction of more appropriate macroscopic and mesoscopic models of transport systems related to the so-called anomalous systems where the corresponding phase space possesses a complicated (fractal) structure. The application of the approach developed in this paper does not change the structure of hydrodynamic and quasihydrodynamic equations, but the modified thermal and calorific state equations and also the transfer coefficients contain two additional free parameters, which are the parameter of the non-additivity of the system and the fractional dimension of the phase space. These parameters can be determined empirically in each particular case from statistical or experimental data, which allows us to simulate the actual variable traffic situation within a continual approach both in regular and crisis cases.