Theory of stress fluctuations

The current status of the theory of stress fluctuations is marked by two circumstances: no currently available formulas are valid for a metallic system, and a series of contradictory formulas remains unresolved. Here we derive formulas for shear- and isotropic-stress energy fluctuations, in the primary statistical mechanics ensembles. These formulas are valid for a classical monatomic system representing a metal or nonmetal, in cubic crystal, amorphous solid, or liquid phases. Current contradictions in fluctuation formulas are resolved through the following observations. First, the expansion of a dynamical variable A in terms of the fluctuations explicit in a given ensemble distribution, for example delta A=a delta N+b delta H in the grand canonical ensemble, is correct if and only if delta A is a function only of delta N and delta H. The common use of this expansion has produced incorrect fluctuation formulas. Second, the thermodynamic fluctuations of Landau and Lifshitz do not correspond to statistical mechanics fluctuations, and the two types of fluctuations have essentially different values.