Gradient and GENERIC time evolution towards reduced dynamics

Multiscale Thermodynamics

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.

Dynamic and Renormalization-Group Extensions of the Landau Theory of Critical Phenomena

We place the Landau theory of critical phenomena into the larger context of multiscale thermodynamics. The thermodynamic potentials, with which the Landau theory begins, arise as Lyapunov like functions in the investigation of the relations among different levels of description. By seeing the renormalization-group approach to critical phenomena as inseparability of levels in the critical point, we can adopt the renormalization-group viewpoint into the Landau theory and by doing it bring its predictions closer to results of experimental observations.

Physically sound, self-learning digital twins for sloshing fluids

In this paper, a novel self-learning digital twin strategy is developed for fluid sloshing phenomena. This class of problems is of utmost importance for robotic manipulation of fluids, for instance, or, in general, in simulation-assisted decision making. The proposed method infers the (linear or non-linear) constitutive behavior of the fluid from video sequences of the sloshing phenomena. Real-time prediction of the fluid response is obtained from a reduced order model (ROM) constructed by means of thermodynamics-informed data-driven learning. From these data, we aim to predict the future response of a twin fluid reacting to the movement of the real container. The constructed system is able to perform accurate forecasts of its future reactions to the movements of the containers. The system is completed with augmented reality techniques, so as to enable comparisons among the predicted result with the actual response of the same liquid and to provide the user with insightful information about the physics taking place.

Variational principles and nonequilibrium thermodynamics

Variational principles play a fundamental role in deriving the evolution equations of physics. They work well in the case of non-dissipative evolution, but for dissipative systems, the variational principles are not unique and not constructive. With the methods of modern nonequilibrium thermodynamics, one can derive evolution equations for dissipative phenomena and, surprisingly, in several cases, one can also reproduce the Euler-Lagrange form and symplectic structure of the evolution equations for non-dissipative processes. In this work, we examine some demonstrative examples and compare thermodynamic and variational techniques. Then, we argue that, instead of searching for variational principles for dissipative systems, there is another viable programme: the second law alone can be an effective tool to construct evolution equations for both dissipative and non-dissipative processes. This article is part of the theme issue 'Fundamental aspects of nonequilibrium thermodynamics'.

Nonequilibrium thermodynamics: emergent and fundamental

How can we derive the evolution equations of dissipative systems? What is the relation between the different approaches? How much do we understand the fundamental aspects of a second law based framework? Is there a hierarchy of dissipative and ideal theories at all? How far can we reach with the new methods of nonequilibrium thermodynamics? This article is part of the theme issue 'Fundamental aspects of nonequilibrium thermodynamics'.