  The general fluctuation theory is reviewed with special attention to the role
played by different ensembles, and is extended to incorporate stationary
metastable states obtained in the long time limit. The fluctuation in a
quantity depends on the nature of the ensemble and contains at most n different
fluctuation contributions, where is the number of fluctuating extensive
quantities in the ensemble. We prove four general theorems and a corollary for
statistical fluctuations valid for any thermodynamic system. We also
demonstrate by two examples that the results of the theory remain valid
regardless of the magnitude of the fluctuations. To avoid certain physical
paradoxes, it is postulated that stationary metastable states like the ideal
glass cannot exist in Nature. We also prove a generalized Nernst theorem valid
at Nernst points at which certain susceptibility like the heat capacity
vanishes. The theorem is no longer restricted to absolute temperature. We
calculate statistical fluctuations in the number of monomers and other physical
quantities of interest in a compressible mixture. We demonstrate that the
density and composition fluctuations are in general not statistically
independent, which is contrary to some recent claims. The standard isothermal
compressibility at constant monomer numbers does not represent the density
fluctuation in all ensembles. We show that the density fluctuation at constant
composition is a meaningless concept, except at absolute zero. We prove a
relation between the weighted monomer number fluctuation and the volume
fluctuation in a multi-component system, which is an extension of a well-known
similar relation for a single component system.
