Locally Anisotropic Kinetic Processes and Thermodynamics in Curved Spaces

TL;DR

This paper develops a kinetic theory framework on curved spacetimes incorporating local anisotropy, unifying relativistic thermodynamics and kinetic equations across various geometric models, with applications to cosmic fluids.

Contribution

It introduces a novel approach to modeling locally anisotropic kinetic processes using anholonomic frames and nonlinear connections on curved spaces, extending thermodynamics and kinetic theory.

Findings

Derived equations of state for pressure and energy in anisotropic thermodynamics.

Calculated transport coefficients like heat conductivity, shear, and volume viscosity.

Applied the framework to determine cosmic fluid transport properties in anisotropic spacetimes.

Abstract

The kinetic theory is formulated with respect to anholonomic frames of reference on curved spacetimes. By using the concept of nonlinear connection we develop an approach to modelling locally anisotropic kinetic processes and, in corresponding limits, the relativistic non-equilibrium thermodynamics with local anisotropy. This lead to a unified formulation of the kinetic equations on (pseudo) Riemannian spaces and in various higher dimensional models of Kaluza-Klein type and/or generalized Lagrange and Finsler spaces. The transition rate considered for the locally anisotropic transport equations is related to the differential cross section and spacetime parameters of anisotropy. The equations of states for pressure and energy in locally anisotropic thermodynamics are derived. The obtained general expressions for heat conductivity, shear and volume viscosity coefficients are applied to determine the transport coefficients of cosmic fluids in spacetimes with generic local anisotropy. We emphasize that such locally anisotropic structures are induced also in general relativity if we are modelling physical processes with respect to frames with mixed sets of holonomic and anholonomic basis vectors which naturally admits an associated nonlinear connection structure.