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Statistical mechanics and the Boltzmann constant

Statistical mechanics, which Boltzmann pioneered, connects macroscopic observations with microscopic behaviors. His statistical explanation of the second law of thermodynamics was a significant achievement, and he provided the current definition of entropy (S = k B ln Ω {\displaystyle S=k_{\rm {B}}\ln \Omega }), where k is the Boltzmann constant and Ω is the number of microstates corresponding to a given macrostate.

Max Planck later named the constant k as the Boltzmann constant in honor of Boltzmann's contributions to statistical mechanics. The Boltzmann constant plays a central role in relating thermodynamic quantities to microscopic properties, and it is now a fundamental constant in physics, appearing in various equations across many scientific disciplines.