Multiscale Thermodynamics

Abstract

Multiscale thermodynamics is a theory of the relations among the levels of investigation of complex systems. It includes the classical equilibrium thermodynamics as a special case, but it is applicable to both static and time evolving processes in externally and internally driven macroscopic systems that are far from equilibrium and are investigated at the microscopic, mesoscopic, and macroscopic levels. In this paper we formulate multiscale thermodynamics, explain its origin, and illustrate it in mesoscopic dynamics that combines levels.

Fluctuating Multiscale Mass Action Law

“…Next, we reduce (n, m) to the state variables (4). Note that the number of reactions q and the number of components p are not related but there are at most p independent reaction steps in each reaction network involving p components.…”

“…If external forces prevent the approach to equilibrium then the equilibrium thermodynamics does not apply. In such situation the approach from an upper to the lower level on which the experimentally observed behavior of the externally driven system is found to be well described provides a basis for another thermodynamics, called rate thermodynamics [3], [4] in which the state space is the space of forces and fluxes. The extended mass-action-law theories introduced in this paper make possible to formulate such theory for chemically reacting systems.…”

Contact Dynamics: Legendrian and Lagrangian Submanifolds

“…Additionally, we can argue that contact framework looks proper for thermodynamics, see, for example, the following incomplete list: [35,[43][44][45]. Accordingly, we also wish to cite [46][47][48][49] for the use of contact geometry for qualitative analysis of reversible-irreversible dynamics under GENERIC (an acronym for General Equation for Non-equilibrium Reversible-Irreversible Coupling) formalism. At the end of this paper, we shall provide some applications of our results on thermodynamics.…”

A nonparametric probabilistic method to enhance PGD solutions with data-driven approach, application to the automated tape placement process

“…However, these surrogate models do not impose naturally physical conditions like the conservation of mass or energy. Therefore, some other PDE fitting techniques are being developed, based on satisfying thermodynamic constraints, using methods like the GENERIC formalism [20,29] or the General Equilibrium for Non-Equilibrium Reversible-Irreversible Coupling [31,38]. However, often engineering applications data is scarce and expensive to generate in sufficient quantities to solely rely on data models.…”