Boltzmann derives P = sigma T^4 theoretically combining Maxwell radiation pressure and Carnot cycles.

Derived u(T) = a T^4 combining Maxwell radiation pressure and thermodynamics.

Boltzmann formulates statistical entropy S = k log W and introduces discrete energy states into …

Introduced discrete energy elements epsilon into combinatorics to calculate probability.

Derived S = k_B log W connecting thermodynamic entropy directly to microstate multiplicity.

Formulated the H-Theorem, proving H quantity decreases over time as gas approaches equilibrium.

Boltzmann formulates the Boltzmann factor exp(-E / k T) for particles in external potential fields.