Related papers: A geometric viewpoint on generalized hydrodynamics
This paper offers an informal instructive introduction to some of the main notions of geometric continuum mechanics for the case of smooth fields. We use a metric invariant stress theory of continuum mechanics to formulate a simple…
We introduce a class of generalized geometric measures of entanglement. For pure quantum states of $N$ elementary subsystems, they are defined as the distances from the sets of $K$-separable states ($K=2,...,N$). The entire set of…
We propose a starting point to the geometric description for the pseudo-gauge ambiguity in relativistic hydrodynamics, showing that it corresponds to the freedom to redefine the thermodynamic equilibrium state of the system. To do this, we…
A simple geometrical model is presented for the gravity-driven motion of a single particle on a rough inclined surface. Adopting a simple restitution law for the collisions between the particle and the surface, we arrive at a model in which…
A gaussian distribution of binding energies, but conditioned to exploit generally available information on packing in liquids, provides a statistical-thermodynamic theory of liquid water that is structurally non-committal, molecularly…
This article gives an overview of recent theoretical and experimental findings concerning the hydrodynamic interaction between liquid-embedded particles in various confined geometries. A simple unifying description emerges, which accounts…
Quantum mechanics is among the most important and successful mathematical model for describing our physical reality. The traditional formulation of quantum mechanics is linear and algebraic. In contrast classical mechanics is a geometrical…
The formal structure of geometrical thermodynamics is reviewed with particular emphasis on the geometry of equilibria submanifolds. On these submanifolds thermodynamic metrics are defined as the Hessian of thermodynamic potentials. Links…
We present a class of thermodynamic systems with constant thermodynamic curvature which, within the context of geometric approaches of thermodynamics, can be interpreted as constant thermodynamic interaction among their components. In…
Hyperbolic conservation laws posed on manifolds arise in many applications to geophysical flows and general relativity. Recent work by the author and his collaborators attempts to set the foundations for a study of weak solutions defined on…
The constraints imposed on hydrodynamics by the structure of gauge and gravitational anomalies are studied in two dimensions. By explicit integration of the consistent gravitational anomaly, we derive the equilibrium partition function at…
In this work we study the general system of geodesic equations for the case of a massive particle moving on an arbitrary curved manifold. The investigation is carried out from the symmetry perspective. By exploiting the parametrization…
We consider multi-gradient fluids endowed with a volumetric internal energy which is a function of mass density, volumetric entropy and their successive gradients. We obtained the thermodynamic forms of equation of motions and equation of…
We revisit the geodesic approach to ideal hydrodynamics and present a related geometric framework for Newton's equations on groups of diffeomorphisms and spaces of probability densities. The latter setting is sufficiently general to include…
According to General Relativity gravity is the result of the interaction between matter and space-time geometry. In this interaction space-time geometry itself is dynamical: it can store and transport energy and momentum in the form of…
We consider the ideal magnetohydrodynamics (MHD) of a shallow fluid layer on a rapidly rotating planet or star. The presence of a background toroidal magnetic field is assumed, and the "shallow water" beta-plane approximation is used. We…
The notion that the geometry of our space-time is not only a static background but can be physically dynamic is well established in general relativity. Geometry can be described as shaped by the presence of matter, where such shaping…
This series of works revisits the geometry, dynamics, and covariant phase space of spherically symmetric spacetimes with the aim of exploring the thermodynamics of spacetime from their dynamical properties. In this first paper, we examine…
The description of general relativistic radiation hydrodynamics in spherical symmetry is presented in natural coordinate choices. For hydrodynamics, comoving coordinates are chosen, and the momentum phase space for the radiation particles…
Recent years have seen a significant progress in the development of general relativistic codes for the numerical solution of the equations of magnetohydrodynamics in spacetimes with high and dynamical curvature. These codes are valuable…