Variational Principles and Nonequilibrium Thermodynamics

Ván, P. and Kovács, R. (2020) Variational Principles and Nonequilibrium Thermodynamics. PHILOSOPHICAL TRANSACTIONS OF THE ROYAL SOCIETY A - MATHEMATICAL, PHYSICAL & ENGINEERING SCIENCES, 378 (2170). pp. 1-16. ISSN 1364-503X (print); 1471-2962 (online)

Text VanKov20.pdf Restricted to Registered users only Download (356kB)

Abstract

Variational principles play a fundamental role in deriving the evolution equations of physics. They work well in the case of non-dissipative evolution, but for dissipative systems, the variational principles are not unique and not constructive. With the methods of modern nonequilibrium thermodynamics, one can derive evolution equations for dissipative phenomena and, surprisingly, in several cases, one can also reproduce the Euler–Lagrange form and symplectic structure of the evolution equations for non-dissipative processes. In this work, we examine some demonstrative examples and compare thermodynamic and variational techniques. Then, we argue that, instead of searching for variational principles for dissipative systems, there is another viable programme: the second law alone can be an effective tool to construct evolution equations for both dissipative and non-dissipative processes.

Actions (login required)

Edit Item