Ensemble and Time Averaging
Configuration given by all positions and momenta
- “phase space” G = (pN,rN)
Configuration variable A(rN,pN)
Ensemble average
- Weighted sum over all members of ensemble
- In general
- For example, canonical ensemble, classical mechanics:
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Time average
- Sum over all states encountered in dynamical trajectory of system
Given by equations of motion
rN shorthand for “positions of all N atoms”
Should average over initial conditions