| 108 |
|
\label{introEq:SM5} |
| 109 |
|
\end{equation} |
| 110 |
|
Where $k_B$ is the Boltzmann constant. Having defined entropy, one can |
| 111 |
< |
also define the temperature of the system using the relation |
| 111 |
> |
also define the temperature of the system using the Maxwell relation |
| 112 |
|
\begin{equation} |
| 113 |
|
\frac{1}{T} = \biggl ( \frac{\partial S}{\partial E} \biggr )_{N,V} |
| 114 |
|
\label{introEq:SM6} |
| 209 |
|
Where the value of an observable is averaged over the length of time |
| 210 |
|
that the simulation is run. This type of measurement mirrors the |
| 211 |
|
experimental measurement of an observable. In an experiment, the |
| 212 |
< |
instrument analyzing the system must average its observation of the |
| 212 |
> |
instrument analyzing the system must average its observation over the |
| 213 |
|
finite time of the measurement. What is required then, is a principle |
| 214 |
|
to relate the time average to the ensemble average. This is the |
| 215 |
|
ergodic hypothesis. |
