Relation Time-Thermodynamics. a Path Integral Approach

TL;DR

This paper explores the relationship between time and thermodynamics using a path integral approach, revealing a complementary dynamics to the algebraic quantum framework and deriving an H-theorem under certain conditions.

Contribution

It introduces a path integral formulation that uncovers a new dynamics related to thermodynamics, complementing the algebraic approach based on Tomita-Takesaki theory.

Findings

Path integral form of the partition function reveals a complementary dynamics.

Defines entropy as a measure of disorder in space-time, aligning with thermodynamics.

Derives an H-theorem in the thermodynamic limit under specific fluctuation conditions.

Abstract

Starting from an algebraic approach of quantum physics it has been shown via the Tomita-Takesaki theorem and the KMS condition that the canonical density matrix contains the dynamics of the system provided we use a rescaling of time. In this paper we show that the path integral form of the partition function reveals a dynamics which is complementary of the one given by the Tomita-Takesaki theorem. To do that we work in the spirit of a Feynman'conjecture. We define the entropy as a measure of the disorder in space time. By using an equilibrium condition we introduce a natural time scale that it is precisely the one appearing in the Tomita-Takesaki theorem. For this time scale depending on the temperature but not on the system properties our definition of entropy is identical to the thermodynamic one. The underlying dynamics associated with the partition function allows us to derive a $\bf{H}$-$theorem$. It is obtained in the thermodynamic limit and provided we are in a regime in which the thermal fluctuations are larger than the quantum ones.