Definitions
from Wiktionary, Creative Commons Attribution/ShareAlike License
 adj. Describing any closed system of constant volume which is thermally isolated from its surroundings, and whose total energy is constant and is known
from The Century Dictionary and Cyclopedia
 In statistical mechanics, of or pertaining to a distribution in phase such that all the systems of an ensemble have the same energy.
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Examples

Per ShangKeng Ma, an entropy can be defined as the logarithm of the phasespace volume explored by the system over a given timescale; the states relevant for thermodynamics (mumble mumble microcanonical mumble mumble) would be the decategorification of the states used at the statisticalmechanical level.

Indefinitely many distinct microcanonical ensembles of a token volume of gas molecules can yield the same mean molecular kinetic energy.

One might then still conjecture that if the system is quasiergodic, the only continuous stationary distribution is microcanonical.

In other words, the only stationary probability with fixed total energy is the microcanonical distribution. Ïmc = Î´ (H (x) ’ E), where Î´ is Dirac's delta function.
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