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This paper contains a fully geometric formulation of the General Equation for Non-Equilibrium Reversible-Irreversible Coupling (GENERIC). Although GENERIC, which is the sum of Hamiltonian mechanics and gradient dynamics, is a framework…

We present and discuss the two-generator framework of nonequilibrium thermodynamics known as GENERIC ("general equation for the nonequilibrium reversible-irreversible coupling"), which is based on geometric concepts and on statistical…

The General Equation for Non-Equilibrium Reversible-Irreversible Coupling (GENERIC) provides structure of mesoscopic multiscale dynamics that guarantees emergence of equilibrium states. Similarly, a lift of the GENERIC structure to iterated…

We propose a novel approach for learning the evolution that employs differentiable neural networks to approximate the full GENERIC structure. Instead of manually choosing the fitted parameters, we learn the whole model together with the…

How to properly describe continuum thermodynamics of binary mixtures where each constituent has its own momentum? The Symmetric Hyperbolic Thermodynamically Consistent (SHTC) framework and Hamiltonian mechanics in the form of the General…

We develop a formalism to discuss the properties of GENERIC systems in terms of corresponding Hamiltonians that appear in the characterization of large-deviation limits. We demonstrate how the GENERIC structure naturally arises from a…

By reformulating the Steepest-Entropy-Ascent (SEA) dynamical model for non-equilibrium thermodynamics in the mathematical language of Differential Geometry, we compare it with the primitive formulation of the GENERIC model and discuss the…

In this paper, we cast damped Timoshenko and damped Bresse systems into a general framework for non-equilibrium thermodynamics, namely the GENERIC (General Equation for Non-Equilibrium Reversible-Irreversible Coupling) framework. The main…

A thermodynamically consistent visco-elastodynamical model at finite strains is derived that also allows for inelasticity (like plasticity or creep), thermal coupling, and poroelasticity with diffusion. The theory is developed in the…

The search for thermodynamic admissibility moreover reveals a fundamental difference between liquids and gases in relativistic fluid dynamics, as the reversible convection mechanism is much simpler for liquids than for gases. In…

The Soft Glassy Rheology (SGR) model is a mesoscopic framework which proved to be very successful in describing flow and deformation of various amorphous materials phenomenologically (e.g. pastes, slurries, foams etc). In this paper, we…

Much of the structure of macroscopic evolution equations for relaxation to equilibrium can be derived from symmetries in the dynamical fluctuations around the most typical trajectory. For example, detailed balance as expressed in terms of…

Recent developments in Macroscopic Fluctuation Theory show that many interacting particle systems behave macroscopically as a combination of a gradient flow with Hamiltonian dynamics. This observation leads to the natural question how these…

The GENERIC theory provides a framework for the description of non-equilibrium phenomena in isolated systems beyond local thermal equilibrium and beyond linear non-equilibrium (i.e., linear relations between thermodynamic forces and…

Formulations of open physical systems within the framework of Non-Equilibrium Reversible/Irreversible Coupling (associated with the acronym "GENERIC") is related in this work with state-space realizations that are given as boundary…

We develop a formulation of global thermodynamics for equilibrium systems under the influence of gravity. The free energy for simple fluids is extended to include a dependence on $(T, V, N, mgL)$, where $L$ represents the vertical system…

The last decades have seen growing interest in connecting principles of thermodynamics with methods from analytical mechanics. The thermodynamic formalism has become an inspiring framework in the study of smooth dynamical systems, and…

In this paper we show how almost cosymplectic structures are a natural framework to study thermodynamical systems. Indeed, we are able to obtain the same evolution equations obtained previously by Gay-Balmaz and Yoshimura (see Entropy,…

We set up a hydrodynamic description of the non-equilibrium dynamics of sine-Gordon quantum field theory for generic coupling. It is built upon an explicit form of the Bethe Ansatz description of general thermodynamic states, with the…

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…