Derivation of Statistical Distributions for non Thermally Equilibrium Systems and Super Conductors

Abstract

Ordinary statistical laws can describe system at equilibrium. But such ordinary statistical laws can no longer describe non equilibrium thermal systems. It cannot also describe systems in which the magnetic or electric or any field is uniform (i.e.at equilibrium). This may explain why super conductor specific heat is hard and very difficult to be explained within the framework of ordinary statistical laws. In this work the laws of plasma fluid dynamics are utilized to derive new statistical distribution laws, unlike ordinary statistical laws, as far as the denominator consists of additional terms beside the ordinary thermal energy term. These derivations shows that the non uniform energy types appear in the numerator, while the uniform energy types appear in the denominator of the power of the exponential term. In this sense all ordinary statistical laws describe systems at thermal equilibrium. The plasma fluid dynamical equations are used to derive Maxwell’s and Gibbs distribution. A useful expression for statistical distribution for physical systems at thermal and potential equilibrium is obtained from plasma equations and shown to coincide with that obtained from ordinary statistical total energy relation. This distribution function beside another one derived from quantum mechanics are utilized to find the lattice specific heat of a super conductor. The plasma equation is also used to find the expression of the electric field and current generated by concentration gradient, beside an expression for the current generated by thermal gradient.