Statistical thermodynamics MOC

Statistical thermodynamics (specifically 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

An ensemble refers to an idealized collection of virtual copies of a system representing every possible 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	$𝜇, 𝑉, 𝑇$

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