Application of a thermodynamical framework for transport analysis to the derivation of Dirac's value function

TL;DR

This paper derives Dirac's value function within a thermodynamical transport framework, validating and generalizing its application to isotope separation and spin magnetization systems, based on entropy of mixing and thermodynamic gradients.

Contribution

It introduces a thermodynamical framework for transport analysis that derives and generalizes Dirac's value function for separative work in various systems.

Findings

Dirac's value function is derived from thermodynamic principles.

The framework validates Dirac's function as a measure of separative work.

Application to spin magnetization demonstrates the framework's generality.

Abstract

From a non-equilibrium thermodynamical framework for transport analysis based on Onsager's Regression Hypothesis, we derive the value function first described by Dirac for isotope separation. This application of the framework is interpreted as both further validation of the transport framework and as a generalization of Dirac's value function. The framework for the analysis of transport phenomena is introduced, first. From the entropy of mixing, and in the presence of gradients in thermodynamic potentials, this framework generates a dynamical transport model from which Dirac's value function is derived as a measure of separative work performed. Dirac's value function is thus shown to be a measure of separative work for systems that are described by the entropy of mixing. As a further demonstration of its generality, the result is applied to a two-quantity, single spatial-dimension spin magnetization system.