Ensemble of states with an exactly specified total energy
Statistical mechanics
Thermodynamics
Kinetic theory
Particle statistics
Spin–statistics theorem
Indistinguishable particles
Maxwell–Boltzmann
Bose–Einstein
Fermi–Dirac
Parastatistics
Anyonic statistics
Braid statistics
Thermodynamic ensembles
NVE Microcanonical
NVT Canonical
µVT Grand canonical
NPH Isoenthalpic–isobaric
NPT Isothermal–isobaric
Models
Debye
Einstein
Ising
Potts
Potentials
Internal energy
Enthalpy
Helmholtz free energy
Gibbs free energy
Grand potential / Landau free energy
Scientists
Maxwell
Boltzmann
Bose
Gibbs
Einstein
Ehrenfest
von Neumann
Tolman
Debye
Fermi
v
t
e
In statistical mechanics, the microcanonical ensemble is a statistical ensemble that represents the possible states of a mechanical system whose total energy is exactly specified.[1] The system is assumed to be isolated in the sense that it cannot exchange energy or particles with its environment, so that (by conservation of energy) the energy of the system does not change with time.
The primary macroscopic variables of the microcanonical ensemble are the total number of particles in the system (symbol: N), the system's volume (symbol: V), as well as the total energy in the system (symbol: E). Each of these is assumed to be constant in the ensemble. For this reason, the microcanonical ensemble is sometimes called the NVE ensemble.
In simple terms, the microcanonical ensemble is defined by assigning an equal probability to every microstate whose energy falls within a range centered at E. All other microstates are given a probability of zero. Since the probabilities must add up to 1, the probability P is the inverse of the number of microstates W within the range of energy,
The range of energy is then reduced in width until it is infinitesimally narrow, still centered at E. In the limit of this process, the microcanonical ensemble is obtained.[1]
^ abGibbs, Josiah Willard (1902). Elementary Principles in Statistical Mechanics. New York: Charles Scribner's Sons.
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