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The entropy force is the collective effect of inhomogeneity in disorder in astatistical many particle system. We demonstrate its presumable effect on oneparticular astrophysical object, the black hole. We then derive the kineticequations of a large system of particles including the entropy force. It adds acollective therefore integral term to the Klimontovich equation for theevolution of the one-particle distribution function. Its integral charactertransforms the basic one particle kinetic equation into an integro-differentialequation already on the elementary level, showing that not only the microscopicforces but the hole system reacts to its evolution of its probabilitydistribution in a holistic way. It also causes a collisionless dissipative termwhich however is small in the inverse particle number and thus negligible.However it contributes an entropic collisional dissipation term. The latter isdefined via the particle correlations but lacks any singularities and thus islarge scale. It allows also for the derivation of a kinetic equation for theentropy density in phase space. This turns out to be of same structure as theequation for the phase space density. The entropy density determines itselfholistically via the integral entropy force thus providing a self-controlledevolution of entropy in phase space.

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