Related papers: Making Sense of the Legendre Transform
The rational Landen transformation is a map on the coefficients of a rational integrand that preserves the value of the integral. This is the rational analog of the classical Landen transformations for elliptic integrals that leads to the…
Motivated by two Legendre-type formulas for overpartitions, we derive a variety of their companions as Legendre theorems for overpartition pairs. This leads to equalities of subclasses of overpartitions and overpartition pairs.
Statistical thermodynamics is valuable as a conceptual structure that shapes our thinking about equilibrium thermodynamic states. A cloud of unresolved questions surrounding the foundations of the theory could lead an impartial observer to…
The rich body of physical theories defines the foundation of our understanding of the world. Its mathematical formulation is based on classical Aristotelian (binary) logic. In the philosophy of science the ambiguities, paradoxes, and the…
In geometrothermodynamics (GTD), to study the geometric properties of the equilibrium space three thermodynamic metrics have been proposed so far. These metrics are obtained by using the condition of Legendre invariance and can be computed…
A class of second-order differential equations commonly arising in physics applications are considered, and their explicit hypergeometric solutions are provided. Further, the relationship with the Generalized and Universal Associated…
Many theories of physical interest, which admit a Hamiltonian description, exhibit symmetries under a particular class of non - strictly canonical transformation, known as dynamical similarities. The presence of such symmetries allows a…
We discuss a subtlety involved in the calculation of multifractal spectra when these are expressed as Legendre-Fenchel transforms of functions analogous to free energy functions. We show that the Legendre-Fenchel transform of a free energy…
Statistical physics has proven to be a very fruitful framework to describe phenomena outside the realm of traditional physics. The last years have witnessed the attempt by physicists to study collective phenomena emerging from the…
In spite of its popularity, it has not been possible to vindicate the conventional wisdom that classical mechanics is a limiting case of quantum mechanics. The purpose of the present paper is to offer an alternative formulation of classical…
One of the main claims of the paper is that Dirac's calculus and broader theories of physics can be treated as theories written in the language of Continuous Logic. Establishing its true interpretation (model) is a model theory problem. The…
Classical and exceptional Lie algebras and their representations are among the most important tools in the analysis of symmetry in physical systems. In this letter we show how the computation of tensor products and branching rules of…
We investigate metric projections and distance functions referring to convex bodies in finite-dimensional normed spaces. For this purpose we identify the vector space with its dual space by using, instead of the usual identification via the…
We introduce a version of the Hamiltonian formalism based on the Clairaut equation theory, which allows us a self-consistent description of systems with degenerate (or singular) Lagrangian. A generalization of the Legendre transform to the…
Quantum advantage is notoriously hard to find and even harder to prove. For example the class of functions computable with classical physics actually exactly coincides with the class computable quantum-mechanically. It is strongly believed,…
The Lagrangian description of mechanical systems and the Legendre Transformation (considered as a passage from the Lagrangian to the Hamiltonian formulation of the dynamics) for point-like objects, for which the infinitesimal configuration…
In some previous papers, a Legendre duality between Lagrangian and Hamiltonian Mechanics has been developed. The (\rho,\eta)-tangent application of the Legendre bundle morphism associated to a Lagrangian L or Hamiltonian H is presented.…
On the basis of information theory, a new formalism of classical non-relativistic mechanics of a mass point is proposed. The particle trajectories of a general dynamical system defined on an (1+n)-dimensional smooth manifold are treated…
Some interactions between classical or quantum fields and matter are known to be irreversible processes. Here we associate an entropy to the electromagnetic field from well-known notions of statistical quantum mechanics, in particular the…
The equilibrium distribution function of a relativistic ideal gas has been derived to include the effect of angular momentum. The result agrees with the one obtained from kinetic theory, and consistent with relativistic thermodynamics. The…