Classical statistical mechanics

Classical statistical mechanics uses probability distributions over classical microscopic states to derive macroscopic properties such as pressure, temperature, and entropy.

Phase space: The space of all possible positions and momenta of a system. A classical system’s microscopic state is represented by a point in phase space.
Boltzmann distribution: The equilibrium probability distribution that weights states by the exponential of their negative energy divided by thermal energy. It gives state probabilities for a classical system in thermal contact with a heat bath.
Maxwell–Boltzmann distribution: The classical equilibrium distribution of particle speeds or velocities in a dilute gas. It predicts the spread of molecular speeds in a classical ideal gas.
Quantum statistical mechanics: The framework that derives macroscopic properties from probability distributions over quantum states. It replaces classical phase-space states when quantum effects cannot be neglected.
James Clerk Maxwell: A Scottish physicist whose work unified electricity and magnetism and advanced kinetic theory. His gas-velocity distribution helped establish a statistical account of molecular motion.
Ensemble (physics): A probability distribution over possible microscopic states of systems prepared under specified macroscopic conditions. Ensembles encode uncertainty about the system’s microscopic state.
Partition function (statistical mechanics): A normalization sum or integral over states whose derivatives yield thermodynamic quantities. The canonical partition function packages the energy statistics needed to calculate equilibrium properties.
Ideal gas: A model gas whose particles have negligible volume and interact only through elastic collisions. Its equation of state follows from a simple statistical treatment of particle motion.
Bose–Einstein statistics: The quantum statistics governing indistinguishable bosons, which can share the same state. Its occupation probabilities differ from classical statistics at low temperatures or high densities.
Ludwig Boltzmann: An Austrian physicist who developed statistical explanations of thermodynamics and molecular gases. His work connected entropy with microscopic probabilities and states.

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Gibbs paradoxRelated: Its naive counting treats exchanged particles as distinct and produces the paradox.