# [SCI] Statistical Mechanics
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**Statistical Mechanics** connects the microscopic behaviour of atoms and molecules to the macroscopic thermodynamic quantities of temperature, pressure, and entropy.
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## Overview
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Ludwig Boltzmann (1872–1877) derived the kinetic theory of gases, proved the H-theorem (entropy increase), and defined entropy as S = k_B log W — the logarithm of the number of accessible microstates. Josiah Willard Gibbs (1902) developed ensemble theory, giving a rigorous framework for systems in thermal equilibrium. The Boltzmann/Gibbs entropy S = −k_B Σ pᵢ log pᵢ is mathematically identical to Shannon's information entropy, a connection that proved profound.
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Statistical mechanics explains phase transitions, chemical equilibria, the third law of thermodynamics, and the foundations of the kinetic theory of gases.
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## Key Figures & Recognition
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- **Ludwig Boltzmann** (1844–1906): Boltzmann equation, entropy formula. No Nobel (predates prize; died by suicide, partly due to opposition from positivists).
- **J. W. Gibbs** (1839–1903): *Elementary Principles in Statistical Mechanics*, 1902.
- **Max Planck** (1858–1947): Applied statistical mechanics to blackbody radiation. Nobel Prize 1918.
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## Seminal Papers
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- Boltzmann, L. "Weitere Studien über das Wärmegleichgewicht unter Gasmolekülen." *Wien. Ber.* 66 (1872).
- Gibbs, J.W. *Elementary Principles in Statistical Mechanics*. Yale University Press, 1902.
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# Parents
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* [SCI] Newtonian Mechanics⏎