  The paper investigates a systematic approach to modeling in nonequilibrium
thermodynamics by focusing upon the notion of interconnections, where we
propose a novel Lagrangian variational formulation of such interconnected
systems by extending the variational principle of Hamilton in mechanics. In
particular, we show how a nonequilibrium thermodynamic system can be regarded
as an interconnected system of primitive physical elements or subsystems
throughout an interconnection. While this approach is new in nonequilibrium
thermodynamics, this idea has been known as a useful tool for the modeling of
complicated systems in networks as well as in mechanics. Hence, the setting
developed in this paper yields a promising direction for building a unifying
description in various areas of modern science via thermodynamic principles,
while being at the same time related to the early developments of variational
mechanics.
