Entropy-Time Relationship in an Isochoric Adiabatic System

The fundamental equation that connects the magnitudes entropy and time has been found out by static thermodynamics for the first time: dS/S = dV I /V 0   = kdτ , V I internal volume. Constant k also equals dT/Tdτ and is an individual characteristic for each isochoric adiabatic system in evolution. The constancy of k does not hold for a nonisochoric adiabatic system. In such manner time is introduced in the frame of thermodynamic variables as a genuine magnitude. The theoretically deduced entropy-time differential equation is empirically upheld by Newton cooling law. It was found in connection with an a priory, uncritical notion of thermodynamic equilibrium that irreversible heat capacity ( C IR = T Δ S/ Δ T ) drawing near to thermodynamic equilibrium is an indicator for the equilibrium. C IR is alike to statistical Boltzmann H in the approach to thermodynamic equilibrium, and the undisclosed connection of H with temperature is presented. The integrated entropy-time equation was modified by rotation of the coordinate axes to fulfill the necessary thermodynamic condition that pertinent irreversible heat ( Q IR = T Δ S ) is smaller than reversible heat ( dQ  =  TdS ), which is not embodied in the primitive S - τ differential equation. This thermodynamically indispensable rotation gives rise to an otherwise naive maximal entropy and an entropy-time maximum point. The transformation conveys a contraction of both entropy and time and is in agreement with the principle of minimal action.