Geometrical and Operational Aspects of Irreversibility

TL;DR

This paper explores the geometric and operational distinctions between reversible and irreversible state changes in classical and quantum dynamical systems, emphasizing the role of isometric transformations and state pair orderings.

Contribution

It introduces a geometric framework for understanding irreversibility and links it to operational criteria distinguishing reversible from irreversible dynamics.

Findings

Reversible changes correspond to isometric transformations.

Irreversibility can be characterized by a pre-ordering of state pairs.

Operational criteria are established to differentiate reversible and irreversible processes.

Abstract

In the statistical description of dynamical systems, an indication of the irreversibility of a given state change is given geometrically by means of a (pre-)ordering of state pairs. Reversible state changes of classical and quantum systems are shown to be represented by isometric state transformations. An operational distinction between reversible and irreversible dynamics is given and related to the geometric characterisation of the associated state transformations.