Ergodic hypothesis

We are often interested in the average of some property across the ensemble of microstates in a macrostate. However, we don’t know which microstate we are in, nor can we configure a particular microstate. The ergodic hypothesis states that this ensemble average of a system equals its time average  —  something we can measure.

f=if(si)p(si)=?1T0Tf(t) ⁣dt. \avg f = \sum_i f(s_i)\, p(s_i) \qeq \frac 1T \int_0^T f(t) \dt.

We assume this holds.