# Approach to Equilibrium, the *H*-Theorem and Irreversibility

# Approach to Equilibrium, the *H*-Theorem and Irreversibility

Like most of the greatest equations in science, the Boltzmann equation is not only beautiful but also generous. Indeed, it delivers a great deal of information without imposing a detailed knowledge of its solutions. In fact, Boltzmann himself derived most if not all of his main results without ever showing that his equation did admit rigorous solutions. This Chapter illustrates one of the most profound contributions of Boltzmann, namely the famous *H*-theorem, providing the first quantitative bridge between the irreversible evolution of the macroscopic world and the reversible laws of the underlying microdynamics.

*Keywords:*
Boltzmann equation, H-theorem, irreversibility, macroscopic physics, microdynamics

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