‘Information therefore trajectories: Entropy and nonequilibrium in the foundations of quantum theory’
by Dr Nicolas Underwood, School of Mathematics and Physics, College of Science, University of Lincoln, Lincoln, UK.
Could quantum probabilities have arisen thermodynamically? Although it remained hidden for some 70 years, it is now widely recognised that de Broglie’s quantum trajectories display a spontaneous thermodynamic relaxation to Born’s rule of quantum probabilities. If this is the ultimate reason for Born’s rule, then we must conjecture an earlier quantum nonequilibrium, perhaps present in the early universe. In other words, the universe could have already undergone a subquantum equivalent of the Boltzmann heat death. Nevertheless, primordial quantum nonequilibrium could have had important consequences in the evolution of the early universe, and may have left experimentally observable traces today.
After reviewing some of this background, we will take a closer look at the statistical mechanics of the relaxation process itself. We’ll ask the question: What are the minimal requirements of a theory for it to relax to the Born rule? Our answer will be a simple geometric principle of information/entropy conservation. Indeed, this conservation doesn’t only provide the necessary framework for thermodynamic relaxation, it also appears to necessitate the existence of trajectories in the first place. To this end, we’ll prove a new theorem: the equivalence of entropy conservation and geometrically constrained trajectories. On this view, such (thermo)dynamical theories may be regarded simply as information + geometry, and we’ll discuss to what extent familiar dynamical theories may be constructed such an information principle.