Concepedia

Variational Principles in Irreversible Thermodynamics with Application to Viscoelasticity

Physical Review · 1955 · 417 citations · 4 references

TL;DR

General differential equations are derived to describe the time history of thermodynamic systems undergoing irreversible transformations. The authors employ Onsager’s principle and generalized free‑energy concepts to formulate variational principles, including a virtual‑work–like principle for reduced variables, which they apply to viscoelastic systems to derive plate‑deflection equations. The resulting equations show that a system’s instantaneous evolution follows a minimum‑rate‑entropy‑production principle, reconcile Prigogine’s stationary‑state theorem, and yield viscoelastic plate‑deflection equations.

Abstract

General differential equations are derived for the time history of a thermodynamic system undergoing irreversible transformations. This is done by using Onsager's principle, and introducing generalized concepts of free energy and thermodynamic potentials. From these equations it is shown that the instantaneous evolution of the system satisfies a principle of minimum rate of entropy production. It is also shown how Prigogine's theorem for the stationary state fits into the present theory. Another variational principle is established for the case where certain variables are ignored in analogy with the methods of virtual work in mechanics. This principle which applies to complex physical-chemical systems is developed more specifically for viscoelastic phenomena, and as an example the differential equations for the deflection of a viscoelastic plate is derived.