Hint for a deduction of the first principle of thermodynamics from microphysics

Abstract

The deduction of the first law of thermodynamics from microphysics involves five main problems of long standing:a) the presence of long-range interactions,b) the nontensor character of the gravitational stress-energy density in the curved space-time,c) the integration of the components of tensors or of a complex (like the gravitational stress-energy density) in a curved space,d) the relativistic formulation of thermodynamics,e) the self-energy of particles. We only face problemsa), b) andc) by a field-theoretical approach to gravitation starting from the ideal, «unrenormalized», flat space-time where the stress-energy density turns out to be a tensor. The energy balance is expressed in terms of electromagnetic (e.m.) and gravitational fields, of stresses due to short-range fields (nuclear fields and Poincare stresses) and of bare-mass densities, which avoid radiation reaction problems and the double computation of the energies associated with the long-range fields (which contribute to real-mass densities). Finally, we express the above quantities in the usual terms of rest-plus-kinetic energies ofparticles andmacroscopic-field energies. However, in this usual form, the first principle of thermodynamics is valid when i) the energies due to the velocity fields of the long-range interactions of the particles of the system considered practically vanish outside the closed boundary surface, and when ii) such «microscopic» energies are much larger than the «macroscopic» energies in the practical region of influence of any particle.