Environment Induced Time Arrow and the Closed Time Path method

TL;DR

This paper demonstrates how environmental initial conditions induce the thermodynamical time arrow using the Closed Time Path formalism in classical and quantum systems, suggesting a shared dynamical origin and a strong quantum-classical coupling.

Contribution

It introduces the Closed Time Path formalism into classical mechanics and explores its implications for understanding the quantum and thermodynamical time arrows.

Findings

Environmental initial conditions induce the thermodynamical time arrow.

The CTP formalism provides a systematic way to handle initial condition problems.

Quantum and thermodynamical time arrows share a common dynamical origin.

Abstract

It is shown in the framework of a harmonic system that the thermodynamical time arrow is induced by the environmental initial conditions in a manner similar to spontaneous symmetry breaking. The Closed Time Path formalism is introduced in classical mechanics to handle Green functions for initial condition problems by the action principle, in a systematic manner. The application of this scheme for quantum systems shows the common dynamical origin of the thermodynamical and the quantum time arrows. It is furthermore conjectured that the quantum-classical transition is strongly coupled.