Ludwig Boltzmann, Transport Equation and the Second
Ludwig Boltzmann, Transport Equation and the Second law K. P. N. Murthy ∗ Theoretical Studies Section, Materials Science Division, Indira Gandhi Centre for Atomic Research, Kalpakkam 603 102, Tamilnadu, INDIA Abstract Ludwig Boltzmann had a hunch that irreversibility exhibited by a macroscopic system arises from the reversible dynamics of its microscopic constituents. He derived a nonlinear integro-differential equation - now called the Boltzmann equation - for the phase space density of the molecules of a dilute fluid. He showed that the Second law of thermodynamics emerges from Newton’s equations of motion. However Boltzmann realized that stosszahlansatz, em- ployed in the derivation, smuggles in an element of stochasticity into the transport equation. He then proposed a fully stochastic description of entropy which laid the foundation for statis- tical mechanics. Recent developments, embodied in different fluctuation theorems, have shown that Boltzmann’s hunch was, in essence, correct. Based on the invited talk given at the arXiv:cond-mat/0601566v3 [cond-mat.stat-mech] 6 Apr 2006 Sixteenth National Symposium on Radiation Physics, Meenakshi College for Women, Chennai, January 18-20, 2006. See A. K. Jena, R. Mathiyarasu and V. Gopalakrishnan (Eds.), Proc. Sixteenth National Symp. Rad. Phys., Indian Society for Radiation Physics (2006)p1. ∗kpn@igcar.gov.in Everything existing in the Universe is the fruit of chance and necessity Diogenes Laertius IX 1 Prologue OLTZMANN transport equation has played an important role in basic and applied sciences. BIt is a nonlinear integro-differential equation for the phase space density of the molecules of a dilute gas. It remains today, an important theoretical technique for investigating non-equilibrium systems.
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