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 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 in both the adiabatically closed cases and open cases. On the continuum side, we illustrate our theory using the example of multicomponent Navier–Stokes–Fourier systems.
Highlights
This paper reviews our recent work on the development of a variational formulation of nonequilibrium thermodynamics, as established in [1,2,3,4]
This is in part due to the lack of a general variational formulation for nonequilibrium thermodynamics that would reduce to the classical Lagrangian variational formulation of mechanics in absence of irreversible processes
While most of the earlier variational approaches mainly underlie the equation for the rate of entropy production, in order to justify the expression of the phenomenological laws governing the irreversible processes involved, our variational approach aims to underlie the complete set of time evolution equations of the system in such a way that it extends the classical Lagrangian formulation in mechanics to nonequilibrium thermodynamic systems including irreversible processes
Summary
This paper reviews our recent work on the development of a variational formulation of nonequilibrium thermodynamics, as established in [1,2,3,4]. This formulation extends to nonequilibrium thermodynamics of the Lagrangian formulation of classical and continuum mechanics that include irreversible processes, such as friction, heat, and mass transfer, chemical reactions, and viscosity
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