Statistical mechanics

Macrostate versus microstate

Macrostate	Microstate
Describe using state variables	Positions and velocities of all particles
Specified by $U,V,N$	Specified by $x_i,v_i$
Entropy gives the most likely macrostate	At constant temperature, each microstate has probability given by the Boltzmann distribution

This is a distribution that gives the probability of a microstate when the system is connected to a big system at temperature $T$ .

$P(microstate~i) = \frac{e^{-E_i/kT}}{\sum_j e^{-E_j/kT}}$