Time & its analytical definition: overcoming inconsistencies of previous results

Recently, a thermodynamic definition of time has been introduced. This definition is useful to find approach some open problems in physics. But, it was obtained by a phenomenological approach and a logical inconsistency appears in the definition. In particular, the definition was based on the ratio of two quantities, the entropy production and its rate, linked one another just by the definition of time. In this paper, this inconsistency is overcome, by using the second law of thermodynamics and Barbour’s mathematical methods, obtaining an analytical result that brings to the same equation of the phenomenological method, but without any logical inconsistency.