Related papers: A Geometric Approach to the Concept of Extensivity…
Thermodynamics provides a unified perspective of thermodynamic properties of various substances. To formulate thermodynamics in the language of sophisticated mathematics, thermodynamics is described by a variety of differential geometries,…
We analyze in the context of geometrothermodynamics a Legendre invariant metric structure in the equilibrium space of an ideal gas. We introduce the concept of thermodynamic geodesic as a succession of points, each corresponding to a state…
In the contact-geometric formulation of classical thermodynamics distinction is made between the energy and entropy representation, which can be resolved by taking homogeneous coordinates for the intensive variables. This results in a…
In this paper we study the ergodic theory and thermodynamic formalism of the geodesic flow on non-compact pinched negatively curved manifolds. We consider two notions of entropy at infinity, the topological and the measure theoretic entropy…
Extended Thermodynamics is a very important theory: for example, it predicts hyperbolicity, finite speeds of propagation waves as well as continuous dependence on initial data. Therefore, it constitutes a significative improvement of…
We develop a geometric foundation of microcanonical thermodynamics in which entropy and its derivatives are determined from the geometry of phase space, rather than being introduced through an a priori ensemble postulate. Once the minimal…
In stationary spacetimes global equilibrium states can be defined, applying the maximum entropy principle, by the introduction of local thermodynamic fields determined solely by geometry. As an example, we study a class of equilibrium…
The physical foundations of a variety of emerging technologies --- ranging from the applications of quantum entanglement in quantum information to the applications of nonequilibrium bulk and interface phenomena in microfluidics, biology,…
In this paper, we discuss the global aspect of the geometric dynamics of volumetric expansion and its application to the problem of the existence in the space-time of compact and complete spacelike hypersurface.
In a recent article we have introduced Friedmann thermodynamics, where certain geometric parameters in Friedmann models are treated like their thermodynamic counterparts (temperature, entropy, Gibbs potential etc.). This model has the…
The fundamental ideas and tools of the global geometric formulation of stress and hyper-stress theory of continuum mechanics are introduced. The proposed framework is the infinite dimensional counterpart of statics of systems having finite…
This manuscript introduces novel approaches to three phenomena. First, we extend the algebraic formulation of kinetic theory within the contact framework by making explicit the gauge freedom, thereby obtaining a formulation in which the…
We construct an explicit representation of the algebra of local diffeomorphisms of a manifold with realistic dimensions. This is achieved in the setting of a general approach to the (quantum) dynamics of a physical system which is…
In this article, we continue the program started in our previous article of exploring an important class of thermodynamic systems from a geometric point of view. In order to model the time evolution of systems verifying the two laws of…
Because only two variables are needed to characterize a simple thermodynamic system in equilibrium, any such system is constrained on a 2D manifold. Of particular interest are the exact 1-forms on the cotangent space of that manifold, since…
We discuss different aspects of the present status of the Statistical Physics focusing the attention on the non-extensive systems, and in particular, on the so called small systems. Multimicrocanonical Distribution and some of its geometric…
In the article it is shown that at presence of fundamental scalar fields determining the masses of the scalar charged particles the global thermodynamic equilibrium (GTE) is compatible with a process of the cosmological expansion of the…
Generalized hydrodynamics (GHD) was proposed recently as a formulation of hydrodynamics for integrable systems, taking into account infinitely-many conservation laws. In this note we further develop the theory in various directions. By…
We analyze gauge theories based on abelian $p-$forms in real compact hyperbolic manifolds. The explicit thermodynamic functions associated with skew--symmetric tensor fields are obtained via zeta--function regularization and the trace…
The spatial resolution of extensive thermodynamic functions is discussed. A physical definition of the spatial resolution based on a spatial analogy of partial molar quantities is advocated, which is shown to be consistent with how…