Everything about Microstate Statistical Mechanics totally explained
In
statistical mechanics, a
microstate describes a specific detailed microscopic configuration of a system, that the system visits in the course of its
thermal fluctuations.
In contrast, the
macrostate of a system refers to its macroscopic properties such as its
temperature and
pressure. In
statistical mechanics, a macrostate is characterized by a
probability distribution on a certain
ensemble of microstates.
This distribution describes the
probability of finding the system in a certain microstate as it's subject to
thermal fluctuations.
Let us now turn to the case of large systems: even if those systems are theoretically able to fluctuate between very different microstates, observing such a fluctuation becomes less and less likely as the size of the system increases. This makes up for the
thermodynamic limit. In this limit, the microstates visited by a system during its
fluctuations all have the same bulk (or macroscopic) properties.
Microscopic definitions of thermodynamic concepts
The definitions of this section link the thermodynamic properties of a system to its distribution on its
ensemble (or set) of microstates. Note that all definitions and expressions of this section are valid even far away from
thermodynamic equilibrium.
In this article we'll consider a system which is distributed on an ensemble of
N microstates.
is the probability associated to the microstate
i, and
is its
energy. Here microstates form a discrete set, which means we're working in
quantum statistical mechanics, and
is an
energy level of the system.
Internal energy
The internal energy is the
mean of the system's
energy »
So that
»
Examples:
Warning: the two above definitions of heat and work are among the few expressions of
statistical mechanics where the sum corresponding to the quantum case can't be converted into an
integral in the classical limit of a
microstate continuum. The reason is that classical microstates are usually not defined in relation to a precise associated quantum microstate, which means that when work changes the energy associated to the energy levels of the system, the energy of classical microstates doesn't follow this change.
Further Information
Get more info on 'Microstate Statistical Mechanics'.
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