HH Diebner and OE Rossler:

*A deterministic entropy based on the instantaneous phase space volume.*

Z. Naturforsch. **53a**, 51-60 (1998).

*Abstract:*

A deterministic entropic measure is derived for the time evolution of Newtonian N-particle systems based on the volume of the instantaneously occupied phase space (IOPS). This measure is found as a natural extension of Boltzmann's entropy. The instantaneous arrangement of the particles is exploited in the form of spatial correlations. The new entropy is a bridge between the time-dependent Boltzmann entropy, formulated on the basis of densities in the one-particle phase space, and the static Gibbs entropy which uses densities in the full phase space. We apply the new concept in a molecular dynamics simulation (MDS) using an exactly time reversible "discrete Newtonian equation of motion" recently derived from the fundamental principle of least action in discretized space-time. The simulation therefore is consistent with micro-time-reversibility. Entropy becomes an exact momentary observable in both time directions in fulfillment of a dream of Boltzmann.