Variational principles and thermodynamics

Abstract

Variational principles play a fundamental role in deriving evolution equations of physics. They are working well in case of nondissipative evolution but for dissipative systems they are not unique, not predictive and not constructive. With methods of modern nonequilibrium thermodynamics, one can derive evolution equations for dissipative phenomena and, surprisingly, can also reproduce the Euler-Lagrange form of the evolution equations for ideal 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, a different program can be more fruitful: the second law alone can be an effective tool to construct both dissipative and nondissipative evolution equations.

References in corpus (6)

• The fourth law of thermodynamics: steepest entropy ascent
• Classical and quantum effective theories
• Thermodynamical extension of a symplectic numerical scheme with half space and time shift demonstrated on rheological waves in solids
• Gradient and GENERIC evolution towards reduced dynamics
• Properties of Conservation-dissipation Formalism of Irreversible Thermodynamics
• Weak invariants in dissipative systems: Action principle and Noether charge for kinetic theory

Cited by in corpus (6)

• Nonequilibrium thermodynamics: emergent and fundamental
• Holographic fluids: a thermodynamic road to quantum physics
• Toward a Universal Theory of Stable Evolution
• A case study of non-Fourier heat conduction using Internal Variables and GENERIC
• Weak invariants in dissipative systems: Action principle and Noether charge for kinetic theory
• Stability of thermally bistable states and their switching in superconducting weak link