Biswajoy Brahmachari
Each distinct way of describing a macroscopic ensemble is called an "arrangement" say. As for example: given macroscopic properties E,V,N, of a collection of molecules of a gas, each set of position and momentum distribution (pi,qi) can be called an arrangement. All such possible arrangements (consistent with specified E,V,N) are a priori equally probable. The observed value of a dynamical variable f is given by fobs= (1/Ω)∑ fr, where fr is the value of f for the rth arrangement. Where Ω is the total number of distinct arrangements which are equally probable by first assumption.
Two fundamental postulates of statistical mechanics.
Over time, an isolated system in a given macroscopic state is equally likely to be found in any possible arrangement of of its microscopic states. A dynamical variable of a macroscopic system can be calculated by taking an appropriate average of that variable over all possible arrangements. While averaging, all distinct arrangement has to be multiplied by the exactly same weight factor.
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