Change, time and information geometry

TL;DR

This paper introduces a novel framework where change and time are intrinsically linked through information geometry, proposing an internal, statistical notion of time derived from the system's own dynamics and entropy principles.

Contribution

It presents a unique, natural dynamical law for irreversible processes based on maximum entropy, redefining time as a measure of change within the system itself.

Findings

Time can be defined internally via change, not externally.

A single dynamical law compatible with maximum entropy is derived.

Time is quantified as change, leading to a new perspective on dynamics.

Abstract

Dynamics, the study of change, is normally the subject of mechanics. Whether the chosen mechanics is ``fundamental'' and deterministic or ``phenomenological'' and stochastic, all changes are described relative to an external time. Here we show that once we define what we are talking about, namely, the system, its states and a criterion to distinguish among them, there is a single, unique, and natural dynamical law for irreversible processes that is compatible with the principle of maximum entropy. In this alternative dynamics changes are described relative to an internal, ``intrinsic'' time which is a derived, statistical concept defined and measured by change itself. Time is quantified change.