From Lagrangian mechanics to nonequilibrium thermodynamics: a variational perspective

Abstract

In this paper, we survey our recent results on the variational formulation of nonequilibrium thermodynamics for the finite dimensional case of discrete systems as well as for the infinite dimensional case of continuum systems. Starting with the fundamental variational principle of classical mechanics, namely, Hamilton's principle, we show, with the help of thermodynamic systems with gradually increasing level complexity, how to systematically extend it to include irreversible processes. In the finite dimensional cases, we treat systems experiencing the irreversible processes of mechanical friction, heat and mass transfer, both in the adiabatically closed and in the open cases. On the continuum side, we illustrate our theory with the example of multicomponent Navier-Stokes-Fourier systems.

7 figures

References in corpus (1)

• Lagrange equations coupled to a thermal equation: mechanics as consequence of thermodynamics

Cited by in corpus (9)

• Symmetries, conservation and dissipation in time-dependent contact systems
• Energy based methods applied in mechanics by using the extended Noether's formalism
• Contact Lagrangian systems subject to impulsive constraints
• Thermodynamically consistent semi-compressible fluids: a variational perspective
• Why and How do Complex Systems Self-Organize at All? Average Action Efficiency as a Predictor, Measure, Driver, and Mechanism of Self-Organization
• An Eulerian hyperbolic model for heat transfer derived via Hamilton's principle: analytical and numerical study
• Thermodynamical Material Networks for Modeling, Planning, and Control of Circular Material Flows
• Non-holonomic constraints: Considerations on the least action principle also from a thermodynamic viewpoint
• A Variational Principle for Extended Irreversible Thermodynamics: Heat Conducting Viscous Fluids