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

Boltzmann distribution

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

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