ﻻ يوجد ملخص باللغة العربية
We propose a variational formulation for the nonequilibrium thermodynamics of discrete open systems, i.e., discrete systems which can exchange mass and heat with the exterior. Our approach is based on a general variational formulation for systems with time-dependent nonlinear nonholonomic constraints and time-dependent Lagrangian. For discrete open systems, the~time-dependent nonlinear constraint is associated with the rate of internal entropy production of the system. We show that this constraint on the solution curve systematically yields a constraint on the variations to be used in the action functional. The proposed variational formulation is intrinsic and provides the same structure for a wide class of discrete open systems. We illustrate our theory by presenting examples of open systems experiencing mechanical interactions, as well as internal diffusion, internal heat transfer, and their cross-effects. Our approach yields a systematic way to derive the complete evolution equations for the open systems, including the expression of the internal entropy production of the system, independently on its complexity. It might be especially useful for the study of the nonequilibrium thermodynamics of biophysical systems.
The recent researches in non equilibrium and far from equilibrium systems have been proved to be useful for their applications in different disciplines and many subjects. A general principle to approach all these phenomena with a unique method of ana
Metriplectic systems are state space formulations that have become well-known under the acronym GENERIC. In this work we present a GENERIC based state space formulation in an operator setting that encodes a weak-formulation of the field equations des
Dirac structures are geometric objects that generalize Poisson structures and presymplectic structures on manifolds. They naturally appear in the formulation of constrained mechanical systems and play an essential role in structuring a dynamical syst
We present a variational formulation for the Navier-Stokes-Fourier system based on a free energy Lagrangian. This formulation is a systematic infinite dimensional extension of the variational approach to the thermodynamics of discrete systems using t
A variational formulation for nonequilibrium thermodynamics was recently proposed in cite{GBYo2017a,GBYo2017b} for both discrete and continuum systems. This formulation extends the Hamilton principle of classical mechanics to include irreversible pro