Dynamical breakdown of time reversal invariance and causality

TL;DR

This paper demonstrates how irreversibility and acausality can emerge in harmonic models due to initial conditions and spectral properties, despite underlying reversible and causal dynamics.

Contribution

It reveals the mechanisms by which time reversal invariance and causality can break down in exactly solvable harmonic systems.

Findings

Initial conditions can break time reversal invariance.

Spectral condensation leads to acausality.

Almost time-independent modes dominate dynamics.

Abstract

Irreversibility and acausality of a sub-system are established in exactly soluble harmonic models with reversible and causal dynamics. It is shown that initial conditions, imposed on some dynamical degrees of freedom may break time reversal invariance for other degrees of freedom. This happens if observations carried out in any large but finite amount of time can not resolve the spectrum of the eliminated degrees of freedom, namely when the spectrum has a condensation point at the ground state. Acausality follows due to the dominance of the dynamics by almost time-independent modes.