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