A generalized kinetic entropy framework for relativistic, drifting, and anisotropic plasmas

In this work, we investigate the kinetic entropy and its flux in fast electron systems under non-local thermodynamic equilibrium. Starting from the relativistic Boltzmann equation, we derive the kinetic entropy evolution equation and decompose the entropy density and entropy flux into the internal energy term and the relative energy term. By applying drifting bi-Maxwellian Jüttner distribution, we systematically compute these quantities as functions of the temperature anisotropy ratio and the dimensionless drift velocity, revealing that relativistic random thermal motion significantly balances the drift velocity and modifies the stress tensor, leading to a screening effect on drift-driven energy transport in the internal energy term within the relativistic regime. This work provides a theoretical foundation for characterizing non-equilibrium thermodynamics and the anisotropy-driven energy redistribution among distinct forms, such as internal energy and work, and kinetic entropy production of fast electrons, benefiting the understanding of their transport and thermalization in tokamaks.