Spontaneous breakdown of the time reversal symmetry

TL;DR

This paper investigates how initial conditions of the environment can lead to spontaneous breaking of time reversal symmetry in effective theories, using the Closed Time Path formalism and a generalized epsilon-prescription.

Contribution

It introduces a novel approach to understanding soft irreversibility by linking environment initial conditions to symmetry breaking through a generalized epsilon-prescription.

Findings

Initial conditions can spontaneously break time reversal symmetry in open systems.

The generalized epsilon-prescription reveals non-uniform convergence causing symmetry breaking.

Effective dynamics of open systems include environment initial conditions leading to irreversibility.

Abstract

The role of the environment initial conditions in the breaking of the time reversal symmetry of effective theories and in generating the soft irreversibility is studied by the help of Closed Time Path formalism. The initial conditions break the time reversal symmetry of the solution of the equation of motion in a trivial manner. When open systems are considered then the initial conditions of the environment must be included in the effective dynamics. This is achieved by means of a generalized $\epsilon$-prescription where the non-uniform convergence of the limit $\epsilon\to0$ leaves behind a spontaneous breakdown of the time reversal symmetry.