Abstract
The definition of the main thermodynamic functions for an adiabatically isolated body with constant internal energy is proposed in the framework of the formalism of the covariant quantum theory with reparametrization invariance of proper time. The modification does not change the dynamic content of the theory at the classical level, but it allows one to define the unitary evolution operator in quantum theory. In this operator, proper time is a measure of the internal movement of the body. The transition to statistical mechanics is carried out by the Wick rotation of proper time in the complex plane. As a result, a representation of the partition function of an isolated body in the form of a Euclidean functional integral on the space of closed trajectories in the configuration space is obtained. For a given internal energy, the average return temperature and free energy are determined, which under lie the thermomechanics of an adiabatically isolated body.
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