Eikonal Representation of Thermodynamics

Abstract

Potentials are integrals governed by a minimum principle. Taking into account the principle of least time the dependence of the position from time arising therefrom and called the geodesic slope excludes the position as a variable of potentials. Instead of using time und position as variables Hilbert's Independent Theorem presents an integral with respect to time whose integrand contains the geodesic slope. The Gibbs thermodynamics suspending the dependence of time is based on differential theorems. From the fact, however, that the Erdmann-WeierstraB comer conditions arising from Hilbert's theorem are in agreement with the relevant thermodynamic conditions of Gibbs we conclude that Hilbert's Independent Integral presents the action of thermodynamics. The thermodynamic action integral is dependent on the lower limit, the least action, and the higher limit presenting the actual state. Because of the reversibility every state between both limits is available. With the reduction of the higher limit into the past we return to the history of all events that happened in the course of milliards of years. The split of this recording into characteristic components is possible with the help of suitable analytical methods. These reveals the history and the origin of thermodynamic compounds. The genetic fingerprint is a well known example.