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Section 4.1 Pre-Quantum

Subsection 4.1.1 Joseph-Louis Lagrange

Years: 1736-1813

Citizenship: Italian-French

Core Contributions:

Classical mechanics definition for the action.

Subsection 4.1.2 Ludwig Boltzmann

Years: 1844-1906

Citizenship: Austrian

Core Contributions:

Boltzmann entropy
Boltzmann distribution
Second Law of Thermodynamics

Before and After Boltzmann: From Mysterious Variable to Profound Understanding.

Before Boltzmann, entropy $S$ was an esoteric-like thermodynamic quantity. He was able to frame this headache of a physical quantity as a combinatorial statement rooted in basic counting and leveraged the fact logarithms have the property that

\begin{equation*} \log{\Omega_A \times \Omega_B} = \log\Omega_A + \log\Omega_B \, . \end{equation*}

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