A DETERMINISTIC ENTROPY-BASED ON THE INSTANTANEOUS PHASE-SPACE VOLUME

A deterministic entropic measure is derived for the time evolution of Newtonian N-particle systems based on the volume of the instantaneousl y occupied phase space (IOPS). This measure is found as a natural exte nsion of Boltzmann's entropy. The instantaneous arrangement of the par ticles is exploited in the form of spatial correlations. The new entro py is a bridge between the time-dependent Boltzmann entropy, formulate d on the basis of densities in the one-particle phase space, and the s tatic Gibbs entropy which uses densities in the full phase space. We a pply the new concept in a molecular dynamics simulation (MDS) using an exactly time reversible ''discrete Newtonian equation of motion'' rec ently derived from the fundamental principle of least action in discre tized space-time. The simulation therefore is consistent with micro-ti me-reversibility. Entropy becomes an exact momentary observable in bot h time directions in fulfillment of a dream of Boltzmann.