Related papers: A Geometric Approach to the Concept of Extensivity…
This paper presents a comprehensive review of geometrical thermodynamics, which employs geometric concepts to study the thermodynamic properties of physical systems. The review covers key topics such as thermodynamic fluctuation theory,…
The morphometric approach is a powerful ansatz for decomposing the chemical potential for a complex solute into purely geometrical terms. This method has proven accuracy in hard spheres, presenting an alternative to comparatively expensive…
Considering a nonlinear charged black hole as a thermodynamics system, we study the geometric description of its phase transitions. Using the formalism of geometrothermodynamics we show that the geometry of the space of thermodynamic…
This paper presents a brief review of the newly developed \emph{Extended Electrodynamics}. The relativistic and non-relativistic approaches to the extension of Maxwell equations are considered briefly, and the further study is carried out…
In this work, we explore the effect at cosmological level of the extra contribution arising from the Geodetic Brane Gravity model within a thermodynamical perspective. As already known, the universe seen as an extended object embedded…
We construct a novel approach, based on thermodynamic geometry, to characterize first-order phase transitions from a microscopic perspective, through the scalar curvature in the equilibrium thermodynamic state space. Our method resolves key…
In the present work, we discuss how the functional form of thermodynamic observables can be deduced from the geometric properties of subsets of phase space. The geometric quantities taken into account are mainly extrinsic curvatures of the…
We define, by an integral of geometric quantities over a spherical shell of arbitrary radius, an invariant gravitational entropy. This definition relies on defining a gravitational energy and pressure, and it reduces at the horizon of both…
Classical vector analysis is the predominant formalism used by engineers of computational electromagnetism, despite the fact that manifold as a theoretical concept has existed for a century. This paper discusses the benefits of manifolds…
Passivity is a fundamental concept that constitutes a necessary condition for any quantum system to attain thermodynamic equilibrium, and for a notion of temperature to emerge. While extensive work has been done that exploits this, the…
I introduce a new geometrical approach to thermo--statistical mechanics. Here I highlight the main physical ideas, and how do they translate into geometrical language. I contrast the present approach with previous…
Classical thermodynamics contains familiar geometric relations associated with cyclic processes, most notably the identification of mechanical work with the area enclosed by a trajectory in the $(P,V)$ plane. We show that the area laws for…
The recent results attained from a thermodynamically conceived numerical scheme applied on wave propagation in viscoelastic/rheological solids are generalized here, both in the sense that the scheme is extended to four spacetime dimensions…
Quantum states defined over a parameter space form a Grassmann manifold. To capture the geometry of the associated gauge structure, gauge-invariant quantities are essential. We employ the projector of a multilevel system to quantify the…
We apply variational principles in the context of geometrothermodynamics. The thermodynamic phase space ${\cal T}$ and the space of equilibrium states ${\cal E}$ turn out to be described by Riemannian metrics which are invariant with…
This tutorial provides an exposition of a flexible geometric framework for high dimensional estimation problems with constraints. The tutorial develops geometric intuition about high dimensional sets, justifies it with some results of…
We examine the dependence of a thermodynamic potential of a fluid on the geometry of its container. If motion invariance, continuity, and additivity of the potential are fulfilled, only four morphometric measures are needed to describe…
Is it actually possible to interpret gravitation as space's property in a pure classical way. Then, we note that extended self-gravitating system equilibrium depends directly on the number of dimension of the space in which it evolves.…
We show that, when we study the coexistence of general relativity with thermodynamics, some physical properties that are usually thought of as holographic and lying in the domain of quantum gravity can actually be accessed even at the…
Thermodynamics is based on a coarse-grained approach, from which its fundamental variables emerge, effectively erasing the complicate details of the microscopic dynamics within a macroscopic system. The strength of Thermodynamics lies in…