Limits of Information Flow Between Classically Interacting Particles

Miles D. Miller-Dickson, Christopher Rose

Miles D. Miller-Dickson, Christopher Rose

Pinning down a precise understanding of information flow within physical interactions remains a central concern to fields such as 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_{0}/2E_{0} in nats/sec, with P_{0} the average power flux between the particle and its environment, and E_{0} 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.

Blagovest A. Nikolov, B. Roy Frieden

Consider a system obeying conservation of flow, as in classical particle flow or in relativistic quantum mechanics. In such cases a probability density function p(r\ensuremath{\Vert}t) may be used to describe the system, where r is particle position and t is time. Let H(t) be the Shannon form of the Boltzmann entropy corresponding to p(r\ensuremath{\Vert}t). It is found that (dH/dt${)}_{\mathrm{max}}$=1/6I(t)d/dt〈${\mathit{r}}^{2}$(t)〉, where I(t) is the Fisher information about the centroid of the system, and 〈${\mathit{r}}^{2}$(t)〉 is the time-dependent mean-square particle position. A corollary is that, for classical particle flow obeying 〈r〉=0, positional uncertainty \ensuremath{\sigma}(t) must ever increase with time.

Charles H. Bennett

A.M. Kowalski, Maria T. Martin, Luciano Zunino +2 more

We investigate the classical limit of the semiclassical evolution with reference to a well-known model that represents the interaction between matter and a given field. This is done by recourse to a special statistical quantifier called the “symbolic transfer entropy”. We encounter that the quantum-classical transition gets thereby described as the sign-reversal of the dominating direction of the information flow between classical and quantal variables.