Eur. Phys. J. Special Topics 224, 927–934 (2015)
https://doi.org/10.1140/epjst/e2015-02436-5

Regular Article

Microscopic local conservation laws for classical fluids

Institut de Physique Théorique, Centre de Saclay, 91191 Gif-sur-Yvette Cedex, France

Received: 20 January 2015
Revised: 7 May 2015
Published online: 17 July 2015

Abstract

The local densities and current densities of conserved quantities are expressed in a tutorial scope, for a fluid under arbitrary off-equilibrium conditions, in terms of the two-particle potential W(r) and of the one- and two-particle densities in phase space f and f₂. When f and f₂ vary significantly over the range of W(r), the density and current density of energy are not defined in a unique fashion, so that conservation of energy can be implemented locally in many different ways. Owing to Galilean invariance, the stress tensor and the heat flux are defined even far from the hydrodynamic regime. This article is supplemented with comments by Y. Pomeau and J. Piasecki.