**Ensemble average** An ensemble is a large number of replications of a system, e.g. all configurations calculated in a simulation.

For a closed system, the ensemble average of some property X of the system is:

<X(t)> = ∑

_{s} X(s)P(s,t) / ∑

_{s}P(s,t)

or in integral notation:

<X(t)> = ∫XP(s,t) ds / ∫ P(s,t) ds

where,

<X> is the average of property X

the sum is over all possible accessible states s

X(s) is the value of the property in state s

P(s) is the probability of finding the system in state s (see Partition function

http://www.oraxcel.com/cgi-bin/yabb2/YaBB.pl?num=1277736407)

For a system with a large number of degrees of freedom, the differences of actual values and the expectationvalue are usually quite small. Further, under equilibrium conditions, P is not a function of t so that X is independent of time and that the expectation value is a time average:

<X> =

_{0}∫

^{T} X(t)dt / T

__See also:__ Ensemble

http://www.oraxcel.com/cgi-bin/yabb2/YaBB.pl?num=1277718050 Partition function

http://www.oraxcel.com/cgi-bin/yabb2/YaBB.pl?num=1277736407/0#0 __Source:__ Kittel, Thermal Physics