Notice that in particular, it states that " the expectation value of " \ hat A " in a single energy eigenstate is equal to the value predicted by a microcanonical ensemble constructed at that energy scale ."
22.
Although the microcanonical ensemble is confined to this surface, it is not necessarily uniformly distributed over that surface : if the gradient of energy in phase space varies, then the microcanonical ensemble is " thicker " ( more concentrated ) in some parts of the surface than others.
23.
Although the microcanonical ensemble is confined to this surface, it is not necessarily uniformly distributed over that surface : if the gradient of energy in phase space varies, then the microcanonical ensemble is " thicker " ( more concentrated ) in some parts of the surface than others.
24.
Also, in some special systems the evolution is ergodic in which case the microcanonical ensemble is equal to the time-ensemble when starting out with a single state of energy ( a time-ensemble is the ensemble formed of all future states evolved from a single initial state ).
25.
The practical effects of energy drift depend on the simulation conditions, the thermodynamic ensemble being simulated, and the intended use of the simulation under study; for example, energy drift has much more severe consequences for simulations of the microcanonical ensemble than the canonical ensemble where the temperature is held constant.
26.
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 : ), the system's volume ( symbol : ), as well as the total energy in the system ( symbol : ).
27.
The microcanonical ensemble is sometimes considered to be the fundamental distribution of statistical thermodynamics, as its form can be justified on elementary grounds such as the principle of indifference : the microcanonical ensemble describes the possible states of an isolated mechanical system when the energy is known exactly, but without any more information about the internal state.
28.
The microcanonical ensemble is sometimes considered to be the fundamental distribution of statistical thermodynamics, as its form can be justified on elementary grounds such as the principle of indifference : the microcanonical ensemble describes the possible states of an isolated mechanical system when the energy is known exactly, but without any more information about the internal state.
29.
When applied to the microcanonical ensemble ( constant particle number, volume, and energy, abbreviated NVE ), using PBC rather than reflecting walls slightly alters the sampling of the simulation due to the conservation of total linear momentum and the position of the center of mass; this ensemble has been termed the " molecular dynamics ensemble " or the NVEPG ensemble.
30.
:general comments : derivations for the microcanonical ensemble and canonical ensemble are already given, IMO in a much better fashion, are given in their respective pages . grand canonical ensemble is a stub, but at least everything is correct and one can just add to it . now the article in question apparently proposes to give separate derivations for these ensembles, and is clearly confused, IMO . along with the mistakes i cited, i thought the overall awkwardness and the redundancy warranted deletion . if someone thinks my judgement of the article is overly harsh and think it's salvagable, that's fine with me . as long as the information on there is correct.
