title: Extensivity and additivity of the Kolmogorov-Sinai entropy for simple fluids.
abstract: According to the van der Waals picture, attractive and repulsive forces play distinct roles in the structure of simple fluids. Here, we examine their roles in dynamics; specifically, in the degree of deterministic chaos using the Kolmogorov-Sinai (KS) entropy rate and the spectra of Lyapunov exponents. With computer simulations of three-dimensional Lennard-Jones and Weeks-Chandler-Andersen fluids, we find repulsive forces dictate these dynamical properties, with attractive forces reducing the KS entropy at a given thermodynamic state. Regardless of interparticle forces, the maximal Lyapunov exponent is intensive for systems ranging from 200 to 2000 particles. Our finite-size scaling analysis also shows that the KS entropy is both extensive (a linear function of system-size) and additive. Both temperature and density control the "dynamical chemical potential," the rate of linear growth of the KS entropy with system size. At fixed system-size, both the KS entropy and the largest exponent exhibit a maximum as a function of density. We attribute the maxima to the competition between two effects: as particles are forced to be in closer proximity, there is an enhancement from the sharp curvature of the repulsive potential and a suppression from the diminishing free volume and particle mobility. The extensivity and additivity of the KS entropy and the intensivity of the largest Lyapunov exponent, however, hold over a range of temperatures and densities across the liquid and liquid-vapor coexistence regimes.
authors.affiliation: Department of Chemistry, University of Massachusetts Boston, Boston, Massachusetts 02125, USA.
authors.forename: Moupriya
authors.initials: M
authors.lastname: Das
authors.affiliation: Numerical Solutions, Inc., P.O. Box 396, Corvallis, Oregon 97330, USA.
authors.forename: Anthony B
authors.initials: AB
authors.lastname: Costa
authors.affiliation: Department of Chemistry, University of Massachusetts Boston, Boston, Massachusetts 02125, USA.|Department of Physics, University of Massachusetts Boston, Boston, Massachusetts 02125, USA.|Center for Quantum and Nonequilibrium Systems, University of Massachusetts Boston, Boston, Massachusetts 02125, USA.
authors.forename: Jason R
authors.initials: JR
authors.lastname: Green