[[Physics MOC]]
# Statistical thermodynamics MOC

**Statistical thermodynamics** (specifically [[Distribution of microstates at equilibrium|MaxEnt thermodynamics]]) derives the laws for macroscopic phenomena seen in [[Thermodynamics MOC]] from the fundamental postulate that the [[Distribution of microstates at equilibrium]] $M$ is that which maximizes the [[Shannon entropy]] $H[M]$,
and that the thermodynamic [[entropy]] $S = k_{B}H[M]$.

## Concepts

- [[Microstate and macrostate]]
- [[Shannon entropy]]
- [[Distribution of microstates at equilibrium]]

## Ensembles

An **ensemble** refers to an idealized collection of virtual copies of a system representing every possible [[Microstate and macrostate|microstate]] the system might be in.

| Ensemble                     | Situation                                            | Thermodynamic variables |
| ---------------------------- | ---------------------------------------------------- | ----------------------- |
| [[Microcanonical ensemble]]  | Isolated system                                      | $N,V,E$                 |
| [[Canonical ensemble]]       | System in contact with heat reservoir                | $N,V,T$                 |
| [[Grand canonical ensemble]] | System in contact with a heat and particle reservoir | $\mu,V,T$               |

## Statistics

**Statistics**, loosely speaking, refers to the method by which one counts microstates.

- [[Maxwell-Boltzmann statistics]]
- [[Modified Boltzmann approximation]]
- [[Fermi-Dirac statistics]]
- [[Bose-Einstein statistics]]

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