In statistical mechanics, a microcanonical ensemble is the statistical ensemble that is used to represent the possible states of a mechanical system which has an exactly specified total energy. The system is assumed to be isolated in the sense that the system cannot exchange energy or particles with its environment, so that (by conservation of energy) the energy of the system remains exactly known as time goes on. The system's energy, composition, volume, and shape are kept the same in all possible states of the system.

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• In statistical mechanics, a microcanonical ensemble is the statistical ensemble that is used to represent the possible states of a mechanical system which has an exactly specified total energy. The system is assumed to be isolated in the sense that the system cannot exchange energy or particles with its environment, so that (by conservation of energy) the energy of the system remains exactly known as time goes on. The system's energy, composition, volume, and shape are kept the same in all possible states of the system. The macroscopic variables of the microcanonical ensemble are quantities that influence the nature of the system's internal states such as 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). This ensemble is therefore sometimes called the NVE ensemble, as each of these three quantities is a constant of the 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. (en)
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• An ensemble containing only those states within a narrow interval of energy. As the energy width is taken to zero, a microcanonical ensemble is obtained .
• Plot of all possible states of this system. The available stationary states displayed as horizontal bars of varying darkness according to .
• Plot of all possible states of this system. The available physical states are evenly distributed in phase space, but with an uneven distribution in energy; the side-plot displays .
• An ensemble restricted to only those states within a narrow interval of energy. This ensemble appears as a thin shell in phase space. As the energy width is taken to zero, a microcanonical ensemble is obtained.
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• Each panel shows phase space and energy-position space . The particle's Hamiltonian is , with the potential shown as a red curve. The side plot shows the distribution of states in energy.
• Example of microcanonical ensemble for a classical system consisting of one particle in a potential well.
• Example of microcanonical ensemble for a quantum system consisting of one particle in a potential well.
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• Ensemble classical 1DOF all states.png
• Ensemble classical 1DOF microcanonical.png
• Ensemble quantum 1DOF all states.png
• Ensemble quantum 1DOF microcanonical.png
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• In statistical mechanics, a microcanonical ensemble is the statistical ensemble that is used to represent the possible states of a mechanical system which has an exactly specified total energy. The system is assumed to be isolated in the sense that the system cannot exchange energy or particles with its environment, so that (by conservation of energy) the energy of the system remains exactly known as time goes on. The system's energy, composition, volume, and shape are kept the same in all possible states of the system. (en)
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• Microcanonical ensemble (en)
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