Limits of Information Flow Between Classically Interacting Particles

TL;DR

This paper introduces a new measure of information flow between particles and environments, based on mutual information and channel capacity, with implications for understanding thermodynamics and quantum information.

Contribution

It proposes a saddle-point based measure of information flow that provides a lower bound on channel capacity, linking physical power flux to information transfer.

Findings

The measure is given by P/2E in nats/sec, relating power flux and energy.

It offers a lower bound on channel capacity between particles and environments.

Applicable to early-time information flow in thermal baths.

Abstract

Pinning down a precise understanding of information flow within physical interactions remains a central concern to fields like stochastic thermodynamics and quantum information science. In both spheres a careful accounting of bits (or qubits) enables a deeper understanding of the physical nature of information. In this work we propose a measure of information flow as a saddle-point solution of the mutual information. This approach places a lower bound on the channel capacity between a particle and an interacting environment. The measure is given by P/2E in nats/sec, with P the average power flux between the particle and its environment, and E the initial average energy of the particle, all computed in a frame where the particle has zero average momentum. We use a communication theory lens to suggest an associated channel analogy, in which this bound is interpreted as a signal-to-noise ratio. We find that this measure can also quantify early-time information flow for a particle interacting with a thermal bath.