Ludwig Boltzmann, Transport Equation and the Second Law

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, employed 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 statistical mechanics. Recent developments, embodied in different fluctuation theorems, have shown that Boltzmann's hunch was, in essence, correct.