Statistical Mechanics I: Ensembles

a macrostate

A macrostate is the coarse, big-picture description of a system, given by the handful of macroscopic quantities you can actually measure: energy E, volume V, particle number N, temperature T, pressure P. Something like 'one mole of gas at 300 K in a one-litre box' is a macrostate. It says nothing about which molecule sits where; it fixes only the overall, thermodynamic-scale numbers.

Formally, a macrostate is specified by a small set of thermodynamic variables and is realized by an enormous number of microstates, all consistent with those constraints. The count of microstates consistent with a macrostate is its multiplicity, W (or Omega); for an isolated system the natural macrostate variables are (E, V, N), and W = W(E, V, N).

The whole art of statistical mechanics is that a single macrostate conceals a colossal number of microstates: for a mole, W can be of order 10^(10^23). The equilibrium macrostate is simply the one realized by overwhelmingly the largest number of microstates, and its entropy is S = k_B ln W. Which variables count as 'macroscopic' is a modelling choice, tied to what you can control and measure.

'One mole of ideal gas at 300 K in volume V' is a macrostate; it corresponds to astronomically many microstates, all with the same energy and particle number.

A few macroscopic numbers stand in for an incomprehensible number of microstates.

The equilibrium macrostate is not privileged by physics beyond being the most probable one, the macrostate realized by the largest number of microstates.

Also called
macroscopic state宏觀態巨觀狀態