Alessandro Bravetti

Universidad Nacional Autónoma de México

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C. S. López-Monsalvo

Universidad Autónoma Metropolitana

Francisco Nettel

Universidad Nacional Autónoma de México

Marcello Seri

University of Groningen

Diego Tapias

University of Göttingen

Angel García-Chung

Universidad Autónoma Metropolitana

Martín Mijangos

Universidad Nacional Autónoma de México

Federico Zadra

Dynamic Systems (United States)

Orlando Luongo

Al-Farabi Kazakh National University

Lucero Pacheco

Universidad Nacional Autónoma de México

Hernando Quevedo

Universidad Nacional Autónoma de México

Cooperative Institutions

Universidad Nacional Autónoma de México

Institute of Mathematical Sciences

Mathematics Research Center

Consejo Superior de Investigaciones Científicas

Universidad Autónoma Metropolitana

L. N. Gumilyov Eurasian National University

Istituto Nazionale di Fisica Nucleare

Universidad Autónoma de la Ciudad de México

University of Cambridge

Universidad de La Laguna

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Precision cosmology with Padé rational approximations: Theoretical predictions versus observational limits

Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D, Particles, fields, gravitation, and cosmology (2014)

Alejandro Avilés Alessandro Bravetti Salvatore Capozziello Orlando Luongo

We propose a novel approach for parameterizing the luminosity distance, based on the use of rational "Pad\'e" approximations. This new technique extends standard Taylor treatments, overcoming possible convergence issues at high redshifts plaguing standard cosmography. Indeed, we show that Pad\'e expansions enable us to confidently use data over a larger interval with respect to the usual Taylor series. To show this property in detail, we propose several Pad\'e expansions and we compare these approximations with cosmic data, thus obtaining cosmographic bounds from the observable universe for all cases. In particular, we fit Pad\'e luminosity distances with observational data from different uncorrelated surveys. We employ union 2.1 supernova data, baryonic acoustic oscillation, Hubble space telescope measurements and differential age data. In so doing, we also demonstrate that the use of Pad\'e approximants can improve the analyses carried out by introducing cosmographic auxiliary variables, i.e. a standard technique usually employed in cosmography in order to overcome the divergence problem. Moreover, for any drawback related to standard cosmography, we emphasize possible resolutions in the framework of Pad\'e approximants. In particular, we investigate how to reduce systematics, how to overcome the degeneracy between cosmological coefficients, how to treat divergences and so forth. As a result, we show that cosmic bounds are actually refined through the use of Pad\'e treatments and the thus derived best values of the cosmographic parameters show slight departures from the standard cosmological paradigm. Although all our results are perfectly consistent with the $\Lambda$CDM model, evolving dark energy components different from a pure cosmological constant are not definitively ruled out.

10.1103/physrevd.90.043531

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Citations (120)

Thermodynamic curvature and ensemble nonequivalence

Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D, Particles, fields, gravitation, and cosmology (2014)

Alessandro Bravetti Francisco Nettel

In this work we consider thermodynamic geometries defined as Hessians of different potentials and derive some useful formulae that show their complementary role in the description of thermodynamic systems with two degrees of freedom that show ensemble nonequivalence. From the expressions derived for the metrics, we can obtain the curvature scalars in a very simple and compact form. We explain here the reason why each curvature scalar diverges over the line of divergence of one of the specific heats. This application is of special interest in the study of changes of stability in black holes as defined by Davies. From these results we are able to prove on a general footing a conjecture first formulated by Liu, L\"u, Luo and Shao stating that different Hessian metrics can correspond to different behaviors in the various ensembles. We study the case of two thermodynamic dimensions. Moreover, comparing our result with the more standard turning point method developed by Poincar\'e, we obtain that the divergence of the scalar curvature of the Hessian metric of one potential exactly matches the change of stability in the corresponding ensemble.

Hessian matrix

Divergence (linguistics)

10.1103/physrevd.90.044064

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Citations (31)

Cosmographic reconstruction off(T)cosmology

Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D, Particles, fields, gravitation, and cosmology (2013)

Alejandro Avilés Alessandro Bravetti Salvatore Capozziello Orlando Luongo

A cosmographic reconstruction of $f(\mathcal T)$ models is here revised in a model independent way by fixing observational bounds on the most relevant terms of the $f(\mathcal T)$ Taylor expansion. We relate the $f(\mathcal T)$ models and their derivatives to the cosmographic parameters and then adopt a Monte Carlo analysis. The experimental bounds are thus independent of the choice of a particular $f(\mathcal T)$ model. The advantage of such an analysis lies on constraining the dynamics of the universe by reconstructing the form of $f(\mathcal T)$, without any further assumptions apart from the validity of the cosmological principle and the analyticity of the $f(\mathcal T)$ function. The main result is to fix model independent cosmographic constraints on the functional form of $f(\mathcal T)$ which are compatible with the theoretical predictions. Furthermore, we infer a phenomenological expression for $f(\mathcal T)$, compatible with the current cosmographic bounds and show that small deviations are expected from a constant $f(\mathcal T)$ term, indicating that the equation of state of dark energy could slightly evolve from the one of the $\Lambda$CDM model.

10.1103/physrevd.87.064025

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Citations (73)

Contact Hamiltonian mechanics

Annals of Physics (2016)

Alessandro Bravetti Hans Cruz Diego Tapias

Hamiltonian mechanics

Hamiltonian (control theory)

Analytical dynamics

Geometric mechanics

10.1016/j.aop.2016.11.003

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Citations (98)

Conformal Gauge Transformations in Thermodynamics

Entropy (2015)

Alessandro Bravetti C. S. López-Monsalvo Francisco Nettel

In this work we consider conformal gauge transformations of the geometric structure of thermodynamic fluctuation theory. In particular, we show that the Thermodynamic Phase Space is naturally endowed with a non-integrable connection, defined by all those processes that annihilate the Gibbs 1-form, i.e. reversible processes. Therefore the geometry of reversible processes is invariant under re-scalings, that is, it has a conformal gauge freedom. Interestingly, as a consequence of the non-integrability of the connection, its curvature is not invariant under conformal gauge transformations and, therefore, neither is the associated pseudo-Riemannian geometry. We argue that this is not surprising, since these two objects are associated with irreversible processes. Moreover, we provide the explicit form in which all the elements of the geometric structure of the Thermodynamic Phase Space change under a conformal gauge transformation. As an example, we revisit the change of the thermodynamic representation and consider the resulting change between the two metrics on the Thermodynamic Phase Space which induce Weinhold's energy metric and Ruppeiner's entropy metric. As a by-product we obtain a proof of the well-known conformal relation between Weinhold's and Ruppeiner's metrics along the equilibrium directions. Finally, we find interesting properties of the almost para-contact structure and of its eigenvectors which may be of physical interest.

Thermodynamic system

Conformal geometry

Thermodynamic free energy

10.3390/e17096150

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Citations (15)

Thermostat algorithm for generating target ensembles

Physical review. E (2016)

Alessandro Bravetti Diego Tapias

We present a deterministic algorithm called contact density dynamics that generates any prescribed target distribution in the physical phase space. Akin to the famous model of Nosé and Hoover, our algorithm is based on a non-Hamiltonian system in an extended phase space. However, the equations of motion in our case follow from contact geometry and we show that in general they have a similar form to those of the so-called density dynamics algorithm. As a prototypical example, we apply our algorithm to produce a Gibbs canonical distribution for a one-dimensional harmonic oscillator.

Thermostat

10.1103/physreve.93.022139

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Citations (38)

From geometry to coherent dissipative dynamics in quantum mechanics

arXiv (Cornell University) (2021)

Hans Cruz Alessandro Bravetti Angel García-Chung

Starting from the geometric description of quantum systems, we propose a novel approach to time-independet dissipative quantum processes according to which the energy is dissipated but the coherence of the states is preserved. Our proposal consists on extending the standard symplectic picture of quantum mechanics to a contact manifold and then obtaining dissipation using an appropriate contact Hamiltonian dynamics. We work out the case of finite-level systems, for which it is shown by means of the corresponding contact master equation that the resulting dynamics constitutes a viable alternative candidate for the description of this subclass of dissipative quantum systems. As a concrete application, motivated by recent experimental observations, we describe quantum decays in a 2-level system as coherent and continuous processes.

Hamiltonian mechanics

Hamiltonian (control theory)

10.48550/arxiv.2107.14267

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Second order phase transitions and thermodynamic geometry: a general approach

arXiv (Cornell University) (2012)

Alessandro Bravetti Francisco Nettel

In this work we relate the curvature of distinct thermodynamic geometries to the response functions of any thermodynamic system with two degrees of freedom. In this manner it is straightforward to identify which geometry describes more accurately second order phase transitions. According to our results, Quevedo’s metric g II in general behaves better than Weinhold and Ruppeiner’s, although in principle ambiguities might appear. It is possible to analyze the problem of describing second order phase transitions through the scalar curvature from a different perspective. For this, we propose a general criterion starting from a particular form of the curvature scalar.

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Geometric Numerical Integration of Liénard Systems via a Contact Hamiltonian Approach

Mathematics (2021)

Federico Zadra Alessandro Bravetti Marcello Seri

Starting from a contact Hamiltonian description of Li\'enard systems, we introduce a new family of explicit geometric integrators for these nonlinear dynamical systems. Focusing on the paradigmatic example of the van der Pol oscillator, we demonstrate that these integrators are particularly stable and preserve the qualitative features of the dynamics, even for relatively large values of the time step and in the stiff regime.

Hamiltonian (control theory)

Variational integrator

10.3390/math9161960

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Citations (6)

Resting state correlation matrices

Figshare (2023)

Alessandro Bravetti Nadia González‐García Martín Mijangos Lucero Pacheco Roberto Velasco Segura

Resting state correlation matrices from a population of 42 teenagers (23 with Inhaled Substance Abuse Disorder), age range: 13-17 years. ISAD participants were recruited by contacting a Youth Integration Center in Mexico City. The Institutional Review Board at the Hospital Infantil de Mexico Federico Gómez approved the study protocol. Informed consent was obtained from parents or guardians.
The control group is formed with individuals from 1 to 19, while the rest of the individuals are ISAD cases.
This is the base dataset of a study in the process of beeing published. When available, the link to the correspondig paper, where you can find further details for this dataset, will be posted here.

10.6084/m9.figshare.21941681.v4

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