A Lagrangian variational modular approach to thermodynamic systems

The diakoptical method developed by Kron (1963) has been known as a powerful tool in modeling and analyzing large-scale physical systems. The principal idea lies in the process of tearing and interconnection for a physical system, namely, one can reticulate the system into several subsystems, each of which is called a primitive system when it once torn apart from the original system. The original system can be regarded as an interconnected system via the interconnection structure, which is known to be modeled as a Dirac structure. This paper illustrates the idea of a Lagrangian variational modular approach by extending the case in mechanics done by Jacobs and Yoshimura (2014) to the case of thermodynamic systems, by following Gay-Balmaz and Yoshimura (2023), together with examples of non-simple thermodynamic systems with internal heat transfer and mechanical interactions.