Abstract
Several recent works have been devoted to the relationship between transport properties and dynamical chaos in systems of classical statistical mechanics [1, 2]. Since the seminal works by Krylov and Sinai [3], we know that the hard sphere gas presents the property of dynamical instability at the microscopic level of its trajectories. Because of the defocusing character of the collisions, nearby trajectories exponentially separate, a remarkable and general phenomenon which is characterized by the Lyapunov exponents, i. e. the orbit separation rates [4]. Stretching of phase space volumes is followed by folding and dynamical randomness results from the exponential instability. The degree of randomness of a time process is evaluated by the entropy per unit time originally introduced by Shannon to characterize a source of information and thereafter applied to dynamical systems by Kolmogorov and Sinai [5].
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Gaspard, P., Baras, F. (1992). Dynamical Chaos Underlying Diffusion in the Lorentz Gas. In: Mareschal, M., Holian, B.L. (eds) Microscopic Simulations of Complex Hydrodynamic Phenomena. NATO ASI Series, vol 292. Springer, Boston, MA. https://doi.org/10.1007/978-1-4899-2314-1_22
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