# 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 $$T$$.

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