Statistical mechanics theorems

theorem

theorem that, in a Lorenz-invariant local quantum field theory, particles with integer spins are bosons, while particles with half-integer spins are fermions

theorem that time rate of change of density of points in phase space along a Hamiltonian flow line is zero

In classical statistical mechanics, the ' H-theorem', introduced by Ludwig Boltzmann in 1872, describes the tendency of the quantity H (defined below) to decrease in a nearly-ideal gas of molecules. As this quantity H was meant to represent the entropy of thermodynamics, the H-theorem was an early demonstration of the power of statistical mechanics as it claimed to derive the second law of thermodynamics—a statement about fundamentally irreversible processes—from reversible microscopic mechanics. It is thought to prove the second law of thermodynamics, albeit under the assumption of low-entrop

theorem

theorem

theorem about the impossibility of spontaneous symmetry breaking in two-dimensional systems at finite temperature

theorem

no-go theorem in quantum information theory, forbidding some communication during measurement of entangled states