Related papers: Legendre-transform structure derived from quantum …

The aim of this paper is to find the exact solutions of the Schrodinger equation. As is known, the Schrodinger equation can be reduced to the continuum equation. In this paper, using the non-linear Legendre transform the equation of…

Using information theoretic quantities like the Wehrl entropy and Fisher's information measure we study the thermodynamics of the problem leading to Landau's diamagnetism, namely, a free spinless electron in a uniform magnetic field. It is…

In [3], the authors used the Legendre transform to give a tractable method for studying Topological Data Analysis (TDA) in terms of sums of Gaussian kernels. In this paper, we prove a variant for sums of cosine similarity-based kernel…

Legendre transform between thermodynamic quantities such as the Helmholtz free energy and entropy plays a key role in the formulation of the canonical ensemble. In the standard treatment, the transform exchanges the independent variable…

Connections between information theory and thermodynamics have proven to be very useful to establish bounding limits for physical processes. Ideas such as Landauer's erasure principle and information assisted work extraction have greatly…

For "static memory materials" the bulk properties depend on boundary conditions. Such materials can be realized by classical statistical systems which admit no unique equilibrium state. We describe the propagation of information from the…

The canonical structure of theories whose Lagrangian contains higher powers of time derivatives is often obscured by the nonlinear relationship between the velocities and momenta. We use the Dirac formalism and define a generalized Legendre…

The development of powerful numerical techniques has drastically improved our understanding of quantum matter out of equilibrium. Inspired by recent progress in the area of noisy intermediate-scale quantum devices, this paper highlights…

The development of stochastic thermodynamics during the last decades prompted the discovery of novel nonequilibrium relations refining our understanding of the second law in small fluctuating systems and its connection with information…

(abridged) In this paper, we present the issues we consider as essential as far as the statistical mechanics of finite systems is concerned. In particular, we emphasis our present understanding of phase transitions in the framework of…

In this article it will be introduced a new theorem, can be considered a generalization of Hellmann-Feynman theorem[1]. The latter used in conjunction with the quantization of the free energy[2] of a quantum system allows to derive…

Information-theoretic derivations of the formalism of quantum theory have recently attracted much attention. We analyze the axioms underlying a few such derivations and propose a conceptual framework in which, by combining several…

Legendre invariant metrics have been introduced in Geometrothermodynamics to take into account the important fact that the thermodynamic properties of physical systems do not depend on the choice of thermodynamic potential from a geometric…

We investigate fundamental connections between thermodynamics and quantum information theory. First, we show that the operational framework of thermal operations is nonequivalent to the framework of Gibbs-preserving maps, and we comment on…

In this paper we develop the theory of information geometry for single random matrix models, with two goals: proving a Cramer-Rao theorem for estimators on random matrices, and calculating the Legendre transform of pressure and entropy with…

We focus attention on some particular thermodynamic relations (PTR). Using information theory concepts we show that, for a reversible process, microscopic considerations related to these PTR make the concomitant informational contents of…

We derive general upper bounds to pointwise mutual information in terms of stochastic Fisher information and show these bounds average to known results in the literature for bounds to mutual information in terms of Fisher information. These…

We update our understanding of nonlinear Schrodinger equations motivated through information theory. In particular we show that a $q-$deformation of the basic nonlinear equation leads to a perturbative increase in the energy of a system,…

Based on a synthesis of three main ingredients: (i) the Shannon information in nonequilibrium systems, (ii) the semiclassical energy-time quantization rule, and (iii) the quasistatic information-energy correspondence, a new general rule for…

The predictions of the standard model of particle physics are highly successful in spite of the fact that several parts of the underlying quantum field theoretical framework are analytically problematic. Indeed, it has long been suggested,…