Ensemble average

The ensemble average (also ensemble average or ensemble average ) is an average of the statistical physics. It can be used the mean value of a measurement parameter of all elements of an ensemble calculated at a randomly selected.

The ensemble average and the time average value are the same for an ergodic system. The ergodic hypothesis states that thermodynamic systems are ergodic and thus they are identical in a given ensemble of the ensemble average and the particular over infinitely long time average.

In the canonical ensemble for a system with discrete states, the probability to find a system in the state i, given by

In which

The canonical partition function. Thus, the ensemble average of a quantity is given by:

Can the set of states no longer count, but is continuous - for example, if the Hamiltonian of the system of continuous places and continuous speeds depends - as one goes from the sum over the integral by suitable extends the above discrete notation with the phase space element, after which one identifies a Riemann integral:

Postgraduate

• Torsten Fließbach: Statistical Physics. 4th edition. Spectrum, Munich 2007, ISBN 978-3-8274-1684-1.

• Statistical Physics