Summa de varones illustres : en la qual se co[n]tienen muchos dichos sente[n]cias y grandes hazañas y cosas memorables de dozie[n]tos y veynte y quatro famosos ansi Emperadores, como Reyes y Capitanes que ha auido de todas las naciones ... por la orde del A.B.C. y las fundaciones de muchos Reynos y Prouincias ...

Copia digital : Junta de Castilla y León. Consejería de Cultura y Turismo, 2014Precede a tít.: "Con priuillegio imperial"La fecha consta en port.Pie de imprenta tomado del colofón.Marca tip. a fin de texto.Sign.: [cristus]6, A-Z8, [et]8, [cristus]A-[cristus]Z8, 2A-2G8, 2H6Port. a dos tintas con orla y esc. imperial.Texto enmarcado a dos col. con notas marginalesLetra gót. con inic. grab.Port. xil. arquitectónica, con escudo imperial y a dos tintasGrab. xil. arquitectónico enmarcando inicio de texto, h. A

Schroedinger vs. Navier-Stokes

[EN] Quantum mechanics has been argued to be a coarse-graining of some underlying deterministic theory. Here we support this view by establishing a map between certain solutions of the Schroedinger equation, and the corresponding solutions of the irrotational Navier-Stokes equation for viscous fluid flow. As a physical model for the fluid itself we propose the quantum probability fluid. It turns out that the (state-dependent) viscosity of this fluid is proportional to Planck's constant, while the volume density of entropy is proportional to Boltzmann's constant. Stationary states have zero viscosity and a vanishing time rate of entropy density. On the other hand, the nonzero viscosity of nonstationary states provides an information-loss mechanism whereby a deterministic theory (a classical fluid governed by the Navier-Stokes equation) gives rise to an emergent theory (a quantum particle governed by the Schroedinger equation).Fernández De Córdoba, P.; Isidro San Juan, JM.; Vazquez Molina, J. (2016). Schroedinger vs. Navier-Stokes. Entropy. 18(1):1-11. doi:10.3390/e18010034S11118

Hyperbolic space in the Newtonian limit: The cosmological constant

[EN] In this paper, the cosmological constant and the Boltzmann entropy of a Newtonian Universe filled with a perfect fluid are computed, under the assumption that spatial sections are copies of 3-dimensional hyperbolic space.This research was supported by Grant No. RTI2018-102256-B-I00 (Spain).Castro-Palacio, JC.; Fernández De Córdoba, P.; Gallego Torromé, R.; Isidro, J. (2022). Hyperbolic space in the Newtonian limit: The cosmological constant. International Journal of Modern Physics D. 31(09):2250072-1-2250072-11. https://doi.org/10.1142/S02182718225007292250072-12250072-11310

The irreversible quantum

We elaborate on the existing notion that quantum mechanics is an emergent phenomenon, by presenting a thermodynamical theory that is dual to quantum mechanics. This dual theory is that of classical irreversible thermodynamics. The linear regime of irreversibility considered here corresponds to the semiclassical approximation in quantum mechanics. An important issue we address is how the irreversibility of time evolution in thermodynamics is mapped onto the quantum-mechanical side of the correspondence.Fernández De Córdoba Castellá, PJ.; Isidro San Juan, JM.; Perea-Córdoba, MH.; Vázquez Molina, J. (2015). The irreversible quantum. International Journal of Geometric Methods in Modern Physics. 12(1). doi:10.1142/S0219887815500139S12

Vortex transmutation

Using group theory arguments and numerical simulations, we demonstrate the possibility of changing the vorticity or topological charge of an individual vortex by means of the action of a system possessing a discrete rotational symmetry of finite order. We establish on theoretical grounds a "transmutation pass rule'' determining the conditions for this phenomenon to occur and numerically analize it in the context of two-dimensional optical lattices or, equivalently, in that of Bose-Einstein condensates in periodic potentials.Comment: 4 pages, 4 figure

Emergent quantum mechanics as a thermal ensemble

It has been argued that gravity acts dissipatively on quantum-mechanical systems, inducing thermal fluctuations that become indistinguishable from quantum fluctuations. This has led some authors to demand that some form of time irreversibility be incorporated into the formalism of quantum mechanics. As a tool toward this goal, we propose a thermodynamical approach to quantum mechanics, based on Onsager s classical theory of irreversible processes and Prigogine s nonunitary transformation theory. An entropy operator replaces the Hamiltonian as the generator of evolution. The canonically conjugate variable corresponding to the entropy is a dimensionless evolution parameter. Contrary to the Hamiltonian, the entropy operator is not a conserved Noether charge. Our construction succeeds in implementing gravitationally-induced irreversibility in the quantum theory.Fernández De Córdoba Castellá, PJ.; Isidro San Juan, JM.; Perea, MH. (2014). Emergent quantum mechanics as a thermal ensemble. International Journal of Geometric Methods in Modern Physics. 11(8):1450068-1450084. doi:10.1142/S0219887814500686S14500681450084118ACOSTA, D., FERNÁNDEZ DE CÓRDOBA, P., ISIDRO, J. M., & SANTANDER, J. L. G. (2012). AN ENTROPIC PICTURE OF EMERGENT QUANTUM MECHANICS. International Journal of Geometric Methods in Modern Physics, 09(05), 1250048. doi:10.1142/s021988781250048xACOSTA, D., FERNÁNDEZ DE CÓRDOBA, P., ISIDRO, J. M., & SANTANDER, J. L. G. (2013). EMERGENT QUANTUM MECHANICS AS A CLASSICAL, IRREVERSIBLE THERMODYNAMICS. International Journal of Geometric Methods in Modern Physics, 10(04), 1350007. doi:10.1142/s0219887813500072Adler, S. L. (2004). Quantum Theory as an Emergent Phenomenon. doi:10.1017/cbo9780511535277Bertoldi, G., Faraggi, A. E., & Matone, M. (2000). Equivalence principle, higher-dimensional Möbius group and the hidden antisymmetric tensor of quantum mechanics. Classical and Quantum Gravity, 17(19), 3965-4005. doi:10.1088/0264-9381/17/19/302Blasone, M., Jizba, P., & Scardigli, F. (2009). Can quantum mechanics be an emergent phenomenon? Journal of Physics: Conference Series, 174, 012034. doi:10.1088/1742-6596/174/1/012034Carroll, R. (2010). On The Emergence Theme Of Physics. doi:10.1142/9789814291804Caticha, A. (2011). Entropic dynamics, time and quantum theory. Journal of Physics A: Mathematical and Theoretical, 44(22), 225303. doi:10.1088/1751-8113/44/22/225303Christenson, J. H., Cronin, J. W., Fitch, V. L., & Turlay, R. (1964). Evidence for the2πDecay of theK20Meson. Physical Review Letters, 13(4), 138-140. doi:10.1103/physrevlett.13.138Connes, A., & Rovelli, C. (1994). Von Neumann algebra automorphisms and time-thermodynamics relation in generally covariant quantum theories. Classical and Quantum Gravity, 11(12), 2899-2917. doi:10.1088/0264-9381/11/12/007ELZE, H.-T. (2009). THE ATTRACTOR AND THE QUANTUM STATES. International Journal of Quantum Information, 07(supp01), 83-96. doi:10.1142/s0219749909004700Elze, H.-T. (2009). Symmetry aspects in emergent quantum mechanics. Journal of Physics: Conference Series, 171, 012034. doi:10.1088/1742-6596/171/1/012034Córdoba, P. F. de, Isidro, J. M., & Perea, M. H. (2013). Emergence from irreversibility. Journal of Physics: Conference Series, 442, 012033. doi:10.1088/1742-6596/442/1/012033Gambini, R., García-Pintos, L. P., & Pullin, J. (2011). An axiomatic formulation of the Montevideo interpretation of quantum mechanics. Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics, 42(4), 256-263. doi:10.1016/j.shpsb.2011.10.002GRAY, N., MINIC, D., & PLEIMLING, M. (2013). ON NONEQUILIBRIUM PHYSICS AND STRING THEORY. International Journal of Modern Physics A, 28(07), 1330009. doi:10.1142/s0217751x13300093Hooft, G. ’t. (1999). Quantum gravity as a dissipative deterministic system. Classical and Quantum Gravity, 16(10), 3263-3279. doi:10.1088/0264-9381/16/10/316’t Hooft, G., Rajantie, A., Contaldi, C., Dauncey, P., & Stoica, H. (2007). Emergent Quantum Mechanics and Emergent Symmetries. AIP Conference Proceedings. doi:10.1063/1.2823751HU, B. L. (2011). GRAVITY AND NONEQUILIBRIUM THERMODYNAMICS OF CLASSICAL MATTER. International Journal of Modern Physics D, 20(05), 697-716. doi:10.1142/s0218271811019049Lees, J. P., Poireau, V., Tisserand, V., Garra Tico, J., Grauges, E., Palano, A., … Kerth, L. T. (2012). Observation of Time-Reversal Violation in theB0Meson System. Physical Review Letters, 109(21). doi:10.1103/physrevlett.109.211801Onsager, L. (1931). Reciprocal Relations in Irreversible Processes. I. Physical Review, 37(4), 405-426. doi:10.1103/physrev.37.405Onsager, L., & Machlup, S. (1953). Fluctuations and Irreversible Processes. Physical Review, 91(6), 1505-1512. doi:10.1103/physrev.91.1505Padmanabhan, T. (2010). Thermodynamical aspects of gravity: new insights. Reports on Progress in Physics, 73(4), 046901. doi:10.1088/0034-4885/73/4/046901Padmanabhan, T. (2011). Lessons from classical gravity about the quantum structure of spacetime. Journal of Physics: Conference Series, 306, 012001. doi:10.1088/1742-6596/306/1/012001Penrose, R. (2009). Black holes, quantum theory and cosmology. Journal of Physics: Conference Series, 174, 012001. doi:10.1088/1742-6596/174/1/012001Rovelli, C. (1993). Statistical mechanics of gravity and the thermodynamical origin of time. Classical and Quantum Gravity, 10(8), 1549-1566. doi:10.1088/0264-9381/10/8/015Rovelli, C. (1996). Relational quantum mechanics. International Journal of Theoretical Physics, 35(8), 1637-1678. doi:10.1007/bf02302261Rovelli, C., & Smerlak, M. (2011). Thermal time and Tolman–Ehrenfest effect: ‘temperature as the speed of time’. Classical and Quantum Gravity, 28(7), 075007. doi:10.1088/0264-9381/28/7/075007Smolin, L. (1986). On the nature of quantum fluctuations and their relation to gravitation and the principle of inertia. Classical and Quantum Gravity, 3(3), 347-359. doi:10.1088/0264-9381/3/3/009Smolin, L. (1986). Quantum gravity and the statistical interpretation of quantum mechanics. International Journal of Theoretical Physics, 25(3), 215-238. doi:10.1007/bf00668705Smolin, L. (2012). A Real Ensemble Interpretation of Quantum Mechanics. Foundations of Physics, 42(10), 1239-1261. doi:10.1007/s10701-012-9666-4Verlinde, E. (2011). On the origin of gravity and the laws of Newton. Journal of High Energy Physics, 2011(4). doi:10.1007/jhep04(2011)029Wald, R. M. (1980). Quantum gravity and time reversibility. Physical Review D, 21(10), 2742-2755. doi:10.1103/physrevd.21.2742Wald, R. M. (1999). Gravitation, thermodynamics and quantum theory. Classical and Quantum Gravity, 16(12A), A177-A190. doi:10.1088/0264-9381/16/12a/309Wetterich, C. (2009). Emergence of quantum mechanics from classical statistics. Journal of Physics: Conference Series, 174, 012008. doi:10.1088/1742-6596/174/1/01200

A web-based application for the management and evaluation of tutoring requests in PBL-based massive laboratories

One important steps in a successful project-based-learning methodology (PBL) is the process of providing the students with a convenient feedback that allows them to keep on developing their projects or to improve them. However, this task is more difficult in massive courses, especially when the project deadline is close. Besides, the continuous evaluation methodology makes necessary to find ways to objectively and continuously measure students' performance without increasing excessively instructors' work load. In order to alleviate these problems, we have developed a web service that allows students to request personal tutoring assistance during the laboratory sessions by specifying the kind of problem they have and the person who could help them to solve it. This service provides tools for the staff to manage the laboratory, for performing continuous evaluation for all students and for the student collaborators, and to prioritize tutoring according to the progress of the student's project. Additionally, the application provides objective metrics which can be used at the end of the subject during the evaluation process in order to support some students' final scores. Different usability statistics and the results of a subjective evaluation with more than 330 students confirm the success of the proposed application

Monte Carlo Simulation of a Modified Chi Distribution Considering Asymmetry in the Generating Functions: Application to the Study of Health-Related Variables

[EN] Random variables in biology, social and health sciences commonly follow skewed distributions. Many of these variables can be represented by exGaussian functions; however, in practice, they are sometimes considered as Gaussian functions when statistical analysis is carried out. The asymmetry can play a fundamental role which can not be captured by central tendency estimators such as the mean. By means of Monte Carlo simulations, the effect of a small asymmetry in the generating functions of the chi distribution is studied. To this end, the k generating functions are taken as exGaussian functions. The limits of this approximation are tested numerically for the practical case of three health-related variables: one physical (body mass index) and two cognitive (verbal fluency and short-term memory). This work is in line with our previous works on a physics-inspired mathematical model to represent the reaction times of a group of individuals.This researchwas partially funded by grant number RTI2018-102256-B-I00 of MINECO/FEDER (Spain). N. Ortigosa acknowledges the support from Generalitat Valenciana under grant Prometeo/2017/102, and from Spanish MINECO under grant MTM2016-76647-P.Ortigosa, N.; Orellana-Panchame, M.; Castro-Palacio, JC.; Fernández De Córdoba, P.; Isidro, J. (2021). Monte Carlo Simulation of a Modified Chi Distribution Considering Asymmetry in the Generating Functions: Application to the Study of Health-Related Variables. Symmetry (Basel). 13(6):1-12. https://doi.org/10.3390/sym1306092411213

Monte Carlo Simulation of a Modified Chi Distribution with Unequal Variances in the Generating Gaussians. A Discrete Methodology to Study Collective Response Times

The Chi distribution is a continuous probability distribution of a random variable obtained from the positive square root of the sum of k squared variables, each coming from a standard Normal distribution (mean = 0 and variance = 1). The variable k indicates the degrees of freedom. The usual expression for the Chi distribution can be generalised to include a parameter which is the variance (which can take any value) of the generating Gaussians. For instance, for k = 3, we have the case of the Maxwell-Boltzmann (MB) distribution of the particle velocities in the Ideal Gas model of Physics. In this work, we analyse the case of unequal variances in the generating Gaussians whose distribution we will still represent approximately in terms of a Chi distribution. We perform a Monte Carlo simulation to generate a random variable which is obtained from the positive square root of the sum of k squared variables, but this time coming from non-standard Normal distributions, where the variances can take any positive value. Then, we determine the boundaries of what to expect when we start from a set of unequal variances in the generating Gaussians. In the second part of the article, we present a discrete model to calculate the parameter of the Chi distribution in an approximate way for this case (unequal variances). We also comment on the application of this simple discrete model to calculate the parameter of the MB distribution (Chi of k = 3) when it is used to represent the reaction times to visual stimuli of a collective of individuals in the framework of a Physics inspired model we have published in a previous work