Absolute Time and Temperature in Quantum and Classical Relativistic Mechanics

We present a relativistic quantum mechanics of a point mass with absolute thermodynamic time and temperature, combined to a single complex parameter of evolution. In this theory, the geometric time is introduced as one of space-time coordinates; it does not coincide with the thermodynamic time on the kinematical level. It is established, that the theory allows a consistent dynamics with nontrivial probability density at the limit $\hbar\to 0$. We identify this dynamics with the classical one, and prove its relativistic invariance. It is shown, that the thermodynamical time becomes proportional to the proper time of the point mass in the conventional classical regime of its evolution with the delta-functional distribution of the probability density.