Shannon information increase and rescue in friction

On the standard microscopic model of friction we confirm the common belief that the irreversible entropy production originates from the increase of Shannon information. We reveal that the reversible microscopic dynamics would continuously violate the Gibbsian interchangeability of molecules. The spontaneous restoration of interchangeability constitutes the mechanism of irreversibility. This is the main suggestion of the Letter. We also point out that the irreversible entropy can partially be rescued if the size of the medium is finite. The rescueable entropy is found to be proportional to the square of the Fisher statistical (also called thermodynamic) distance. Introduction. It is commonly trusted that the thermodynamic entropy produced in irreversible processes is identical to the increase of the Shannon information in the underlying microdynamic process. A direct proof is yet missing. The microscopic dynamics is reversible, it preserves the Shannon information. We need a transparent model to resolve this fundamental paradox. In this Letter I discuss the mechanical friction of a thin ‘disc’ perpendicularly driven through a medium with small velocity V . The phenomenological model is a prototype for the whole theory of irreversible processes [1]. Accordingly, the disc moves against the frictional force −ηV where η is the friction constant. If the medium (reservoir) is in thermal equilibrium at inverse temperature β then the rate of thermodynamic entropy production can be written in this form: Ṡ = ηβV 2 . (1) An elementary microscopic model will be considered where the medium is ideal gas of light molecules scattering elastically on both flat surfaces of