Directional information transfer between interacting Brownian particles

TL;DR

This paper explores how mass asymmetry in two interacting Brownian particles causes a directional flow of information, quantified by transfer entropy, revealing fundamental links between physical dynamics and information transfer.

Contribution

It demonstrates that mass asymmetry induces a net directional information flow and analytically relates this to differences in memory and predictability of particle trajectories.

Findings

Net information transfer scales logarithmically with mass ratio.

Mass asymmetry causes a directional information flow from heavier to lighter particle.

Heavier particles act as information sources due to higher inertia and memory.

Abstract

We theoretically investigate how information flows when two particles interact with each other. Understanding the physical mechanisms of directional information flow is crucial for advancing information thermodynamics and stochastic computing. However, the fundamental connection between mechanical motion and causal information transfer remains elusive. To focus only on essential effects of physical dynamics, we examine two interacting Brownian particles confined in a one-dimensional potential. By simulating their Langevin dynamics, we quantify the causal information exchange using transfer entropy. We demonstrate that a mass asymmetry inherently breaks the symmetry of information flow, inducing a net directional transfer from the heavier to the lighter particle. Physically, the heavier particle, possessing larger inertia and higher active information storage, retains the memory of its trajectory longer against thermal fluctuations, thereby acting as a source of information. We analytically clarify that this net transfer is governed by a competition between the difference in memory capacity and the predictability of the particle trajectories. Furthermore, we reveal that the net information flow scales logarithmically with the mass ratio. These findings provide essential insights into the physical significance of transfer entropy and the nature of information flow in general physical systems.