Related papers: Relativisticlike structure of classical thermodyna…
The contact geometric structure of the thermodynamic phase space is used to introduce a novel symplectic structure on the tangent bundle of the equilibrium space. Moreover, it turns out that the equilibrium space can be interpreted as a…
We consider thermodynamics of the van der Waals fluid of quantum systems. We derive general relations of thermodynamic functions and parameters of any ideal gas and the corresponding van der Waals fluid. This provides unambiguous…
Relativistic thermodynamics is treated from the point of view of kinetic theory. It is shown that the generalized J\"uttner distribution suggested in [1] is compatible with kinetic equilibrium. The requirement of compatibility of kinetic…
In this paper we find a connection between the macroscopic classical laws of gases and the quantum mechanical description of molecules, composing an ideal gas. In such a gas, the motion of each individual molecule can be considered…
Starting from a formulation for the $dS$ element that includes movement, and considering the variation of the entropy Lorentz invariant, we found the relativistic transformations for thermodynamic systems that satisfy the three laws of…
The essential postulates of classical thermodynamics are formulated, from which the second law is deduced as the principle of increase of entropy in irreversible adiabatic processes that take one equilibrium state to another. The entropy…
We study geodesics on the parameter manifold, for systems exhibiting second order classical and quantum phase transitions. The coupled non-linear geodesic equations are solved numerically for a variety of models which show such phase…
We elucidate the geometry of quantum adiabatic evolution. By minimizing the deviation from adiabaticity we find a Riemannian metric tensor underlying adiabatic evolution. Equipped with this tensor, we identify a unified geometric…
We study the intriguing analogy between gravitational dynamics of the horizon and thermodynamics for the case of nonstationary radiating spherically symmetric black holes both in four dimensions and higher dimensions. By defining all…
Using the formalism of geometrothermodynamics to derive a fundamental thermodynamic equation, we construct a cosmological model in the framework of relativistic cosmology. In a first step, we describe a system without thermodynamic…
There is a long-standing question as to whether and to what extent it is possible to describe nonequilibrium systems in stationary states in terms of global thermodynamic functions. The positive answers have been obtained only for…
These lecture notes present an overview of equilibrium statistical mechanics of classical fluids, with special applications to the structural and thermodynamic properties of systems made of particles interacting via the hard-sphere…
We show the equivalence of several characterizations of relative hyperbolicity for metric spaces, and obtain extra information about geodesics in a relatively hyperbolic space. We apply this to characterize hyperbolically embedded subgroups…
A simple and effective approach to thermodynamics is suggested, which solves the major difficulties in the traditional presentation of the subject. The internal energy is introduced from the behavior of deformable bodies, whereas the…
We study steady-state properties of inelastic gases in two-dimensions in the presence of an energy source. We generalize previous hydrodynamic treatments to situations where high and low density regions coexist. The theoretical predictions…
The classifying space of inertial reference frames in special relativity is naturally hyperbolic. There is a remarkable interplay between central elements of hyperbolic geometry and those of special relativity -- which, to a certain extent,…
In a first part the scope of classical thermodynamics and statistical mechanics is discussed in the broader context of formal dynamical systems, including computer programmes. In this context classical thermodynamics appears as a particular…
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…
In the paper, the principal aspects of the mathematical theory of equilibrium thermodynamics are distinguished. It is proved that the points of degeneration of a Bose gas of fractal dimension in the momentum space coincide with critical…
An irreversible thermodynamical theory of solids is presented where the kinematic quantities are defined in an automatically objective way. Namely, auxiliary elements like reference frame, reference time and reference configuration are…