Microcanonical ensemble

The statistical-mechanical model of an isolated system with fixed energy, volume, and particle number, assigning equal probability to every accessible microstate.

Microstate: A complete specification of a system’s microscopic configuration, such as its particles’ positions and momenta. The ensemble assigns probabilities to these configurations, restricted to the fixed macroscopic constraints.
Thermodynamic system: A specified quantity of matter or region of space studied through macroscopic variables and thermodynamic laws. The ensemble models one such system while holding its defining extensive quantities fixed.
Canonical ensemble: A statistical-mechanical model of a system at fixed temperature that exchanges energy with a heat reservoir. Unlike the microcanonical ensemble, it permits energy fluctuations and weights states by the Boltzmann factor.
Molecular dynamics: A computational method that simulates particle motion by numerically integrating equations of motion. Energy-conserving simulations approximate microcanonical evolution when no thermostat is applied.
Phase space: The space of all possible positions and momenta of a classical system. Accessible microstates occupy the portion of phase space compatible with the fixed energy.
Energy conservation: The physical principle that total energy remains constant in an isolated system. Its fixed-energy condition confines accessible states to a single energy value or narrow shell.
Grand canonical ensemble: A statistical-mechanical model in which a system exchanges energy and particles with reservoirs at fixed temperature and chemical potential. It relaxes both fixed-energy and fixed-particle-number constraints.
Isolated system: A physical system that exchanges neither matter nor energy with its surroundings. This is the physical idealization represented by the ensemble’s fixed conserved quantities.
Density of states: The number of states available per interval of energy or another specified quantity. It counts how many microstates contribute at the ensemble’s fixed energy.
Ergodic hypothesis: The hypothesis that a system’s long-time trajectory explores its accessible energy surface sufficiently thoroughly. It can justify estimating equilibrium probabilities from time averages over accessible states.

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