Entropic formulation of relativistic continuum mechanics

Details Entropic formulation of relativistic continuum mechanics Entropic formulation of relativistic continuum mechanics

2011-02-08

arxiv.org/abs/1102.1557v4

Phys.Rev.E84:026315,2011

Physics

High Energy Physics

High Energy Physics - Theory

29 pages, 5 figures; v2: discussions on reversible processes are improved; v3: added references, to appear in Physical Review

Scientific paper

10.1103/PhysRevE.84.026315

An entropic formulation of relativistic continuum mechanics is developed in the Landau-Lifshitz frame. We introduce two spatial scales, one being the small scale representing the linear size of each material particle and the other the large scale representing the linear size of a large system which consists of the material particles and is to linearly regress to the equilibrium. We propose a local functional which is expected to represent the total entropy of the larger system and require the entropy functional to be maximized in the process of linear regression. We show that Onsager's original idea on linear regression can then be realized explicitly as current conservations with dissipative currents in the desired form. We demonstrate the effectiveness of this formulation by showing that one can treat a wide class of relativistic continuum materials, including standard relativistic viscous fluids and relativistic viscoelastic materials.

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