A Note on the Entropy Force in Kinetic Theory and Black Holes

TL;DR

This paper explores the entropy force's role in black hole physics, deriving a kinetic equation that incorporates collective effects, leading to a holistic and self-consistent description of entropy evolution in phase space.

Contribution

It introduces a new kinetic equation including the entropy force, revealing its integral and collective effects on the evolution of particle systems and black holes.

Findings

Entropy force adds an integral term to kinetic equations.

The resulting equation is an integro-differential form.

Entropy evolution is self-controlled via the entropy force.

Abstract

The entropy force is the collective effect of inhomogeneity in disorder in a statistical many particle system. We demonstrate its presumable effect on one particular astrophysical object, the black hole. We then derive the kinetic equations of a large system of particles including the entropy force. It adds a collective therefore integral term to the Klimontovich equation for the evolution of the one-particle distribution function. Its integral character transforms the basic one particle kinetic equation into an integro-differential equation already on the elementary level, showing that not only the microscopic forces but the hole system reacts to its evolution of its probability distribution in a holistic way. It also causes a collisionless dissipative term which however is small in the inverse particle number and thus negligible. However it contributes an entropic collisional dissipation term. The latter is defined via the particle correlations but lacks any singularities and thus is large scale. It allows also for the derivation of a kinetic equation for the entropy density in phase space. This turns out to be of same structure as the equation for the phase space density. The entropy density determines itself holistically via the integral entropy force thus providing a self-controlled evolution of entropy in phase space.