Irreversible thermodynamics, quantum mechanics and intrinsic time scales

Abstract

AbstractIt is often assumed that phenomenology is a rather weak tool for the analysis of natural systems because it lacks generality. However, in a series of papers we have developed a phenomenological calculus based upon a general theory of measurement and mathematical representations (or, equivalently, upon system response as a bilinear form) which has a broad range of application. The present paper illustrates its power and versatility by demonstrating that irreversible thermodynamics and quantum mechanics are homomorphic. This result is, in itself, interesting since it shows that a large class of dissipative, deterministic systems are homomorphic to a large class of ideal, stochastic systems. In both cases, the metrical structure of the phenomenological calculus allows us to define a “proper time” intrinsic to the system dynamics. With this intrinsic time, a dynamics of aging can be defined upon the system's parameter space. In this context, Schrödinger's equation is seen as a dynamics of aging