Thermodynamic and quantum length scales in a geometrical extension of statistical mechanics

A relativistic self-diffusion theory, recently proposed to investigate scaling laws of macromolecules in solution, is reformulated by means of geometrical quantities. The mean chain displacement is regarded as a volume (v), localized in an extension (a larger volume V) by a shape (φ), and affecting extension and shape. Lorentz transformations applied to v, V and φ returns a constraint, which establishes a link between different length scales, and provides with a simple extension of statistical mechanics. The Boltzmann factor achieved, generalized according to the wavefunction concept in quantum mechanics, enables us to obtain a length-dependent heat capacity equation.