Brownian Motion as a Route to Statistical Mechanics and to a Tentative Quantum Communication Theory

摘要

The author considers a molecular bath in statistical equilibrium at temperature T. A heavy particle in this bath undergoes Brownian motion, acquiring a mean kinetic energy 3kT/2 regardless of the nature of its encounters with the molecules of the bath. Specifying that these encounters are elastic collisions occurring only for molecules in a narrow band of relative velocities, he uses Brownian-motion principles to show, in one-dimensional examples, that the number density of molecules in that band is determined by the kT/2 mean kinetic energy of the Brownian particle. He thus obtains the one-dimensional equilibrium energy distribution for classical and quantum molecules, at the price of assuming no more than the relation between the first two moments (the mean count and the mean-square count of particles per unit time) of the appropriate microstatistics. Toward a quantum communication theory, he considers the Brownian particle to be a narrow-reflection-band filter freely sliding in an ideal transmission line terminated by matched loads at temperature T. He inserts Planck's constant h into the mathematics so that the resulting one-dimensional electromgnetic spectrum is Planckian for temperature T. The result gives the following rule of thumb for quantum communication theoretic problems classically entailing no more than power spectrums S(f) and their squares S2(f): add hf S(f) to S2(f) to produce the quantum version. The merits of this approach, of the general method, and of some related problems are discussed. (Author)