Limits of Information Flow Between Classically Interacting Particles

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.