A scale-invariant model of statistical mechanics and modified forms of the first and the second laws of thermodynamics

Abstract

A scale-invariant statistical theory of fields is presented that leads to invariant definition of density, velocity, temperature, and pressure. The definition of Boltzmann constant is introduced as k k = k = m k ν k c = 1.381 · 10 −23 J·K −1, suggesting that the Kelvin absolute temperature scale is equivalent to a length scale. Two new state variables called the reversible heat Q rev = TS and the reversible work W rev = PV are introduced. The modified forms of the first and second law of thermodynamics are presented. The microscopic definition of heat (work) is presented as the kinetic energy due to the random (peculiar) translational, rotational, and pulsational motions. The Gibbs free energy of an element at scale β is identified as the total system energy at scale (β − 1), thus leading to an invariant form of the first law of thermodynamics U β = Q β − W β + N eβ U β−1 .