The Kolmogorov-Sinai Entropy for Dilute Gases in Equilibrium

Abstract

We use the kinetic theory of gases to compute the Kolmogorov-Sinai entropy per particle for a dilute gas in equilibrium. For an equilibrium system, the KS entropy, h_KS is the sum of all of the positive Lyapunov exponents characterizing the chaotic behavior of the gas. We compute h_KS/N, where N is the number of particles in the gas. This quantity has a density expansion of the form h_KS/N = aν[-\ln{\tilde{n}} + b + O(\tilde{n})], where νis the single-particle collision frequency and \tilde{n} is the reduced number density of the gas. The theoretical values for the coefficients a and b are compared with the results of computer simulations, with excellent agreement for a, and less than satisfactory agreement for b. Possible reasons for this difference in b are discussed.

15 pages, 2 figures, submitted to Phys. Rev. E

Cited by in corpus (30)

• Thermodynamic formalism for systems with Markov dynamics
• Chaotic properties of systems with Markov dynamics
• Temperature dependence of butterfly effect in a classical many-body system
• Hamiltonian dynamics, nanosystems, and nonequilibrium statistical mechanics
• The Fractality of the Hydrodynamic Modes of Diffusion
• Brownian motion and diffusion: from stochastic processes to chaos and beyond
• Largest Lyapunov exponents for lattices of interacting classical spins
• Theory of Transport Processes and the Method of the Nonequilibrium Statistical Operator
• Chaotic Properties of Dilute Two and Three Dimensional Random Lorentz Gases I: Equilibrium Systems
• Chaotic Properties of Dilute Two and Three Dimensional Random Lorentz Gases II: Open Systems
• Fractal Dimensions of the Hydrodynamic Modes of Diffusion
• Lyapunov instabilities in lattices of interacting classical spins at infinite temperature
• Viscosity in the escape-rate formalism
• When do tracer particles dominate the Lyapunov spectrum?
• B. B. G. K. Y. Hierarchy Methods for Sums of Lyapunov Exponents for Dilute Gases
• The Lyapunov spectrum of the many-dimensional dilute random Lorentz gas
• What does dynamical systems theory teach us about fluids?
• The Kolmogorov-Sinai entropy for dilute systems of hard particles in equilibrium
• Front propagation techniques to calculate the largest Lyapunov exponent of dilute hard disk gases
• Comment on ``Lyapunov Exponent of a Many Body System and Its Transport Coefficients''
• On the Kolmogorov-Sinai entropy of many-body Hamiltonian systems
• Lyapunov spectra of billiards with cylindrical scatterers: comparison with many-particle systems
• Kinetic Theory of Cluster Dynamics
• Poles of hydrodynamic spectral functions and Einstein-Helfand formulas for transport coefficients
• Classical Dynamics of Harmonically Trapped Interacting Particles
• The entropy of co-compact open covers
• Radius of curvature approach to the Kolmogorov-Sinai entropy of dilute hard particles in equilibrium
• Chaoticity of the Wet Granular Gas
• Equivalence of kinetic-theory and random-matrix approaches to Lyapunov spectra of hard-sphere systems
• Role of chaos for the validity of statistical mechanics laws: diffusion and conduction