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

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. 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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). 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Entropy, Topological Theories and Emergent Quantum Mechanics

[EN] The classical thermostatics of equilibrium processes is shown to possess a quantum mechanical dual theory with a finite dimensional Hilbert space of quantum states. Specifically, the kernel of a certain Hamiltonian operator becomes the Hilbert space of quasistatic quantum mechanics. The relation of thermostatics to topological field theory is also discussed in the context of the approach of the emergence of quantum theory, where the concept of entropy plays a key role.Research supported by grant No. ENE2015-71333-R (Spain).Cabrera, D.; Fernández De Córdoba Castellá, PJ.; Isidro San Juan, JM.; Vazquez Molina, J. (2017). Entropy, Topological Theories and Emergent Quantum Mechanics. Entropy. 19(3). https://doi.org/10.3390/e19030087S19

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

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

Exact solution for the time-dependent temperature field in dry grinding: application to segmental wheels

We present a closed analytical solution for the time evolution of the temperature field in dry grinding for any time-dependent friction profile between the grinding wheel and the workpiece. We base our solution in the framework of the Samara-Valencia model Skuratov et al., 2007, solving the integral equation posed for the case of dry grinding. We apply our solution to segmental wheels that produce an intermittent friction over the workpiece surface. For the same grinding parameters, we plot the temperature fields of up- and downgrinding, showing that they are quite different from each other. © 2011 J. L. Gonzlez-Santander et al.The authors wish to thank the financial support received from Generalitat Valenciana under Grant GVA 3012/2009 and from Universidad Politecnica de Valencia under Grant PAID-06-09.González-Santander Martínez, JL.; Valdes Placeres, JM.; Isidro San Juan, JM. (2011). Exact solution for the time-dependent temperature field in dry grinding: application to segmental wheels. Mathematical Problems in Engineering. 1-28. doi:10.1155/2011/927876S12

Percentile Study of chi Distribution. Application to Response Time Data.

As a continuation of our previous work, where a Maxwell-Boltzmann distribution was found to model a collective's reaction times, in this work we will carry out a percentile study of the χ distribution for some freedom ranging from k = 2 to k = 10. The most commonly used percentiles in the biomedical and behavioral sciences have been included in the analysis. We seek to provide a look-up table with percentile ratios, taken symmetrically about the median, such that this distribution can be identified in practice in an easy way. We have proven that these ratios do not depend upon the variance chosen for the k generating Gaussians. In general, the χ probability density, generalized to take any value of the variance, represents an ideal gas in a k-dimensional space. We also derive an approximate expression for the median of the generalized χ distribution. In the second part of the results, we will focus on the practical case of k = 3, which represents the ideal gas in physics, and models quite well the reaction times of a human collective. Accurately, we will perform a more detailed scrutiny of the percentiles for the reaction time distribution of a sample of 50 school-aged children (7200 reaction times)

Machinery Failure Approach and Spectral Analysis to Study the Reaction Time Dynamics over Consecutive Visual Stimuli: An Entropy-Based Model.

The reaction times of individuals over consecutive visual stimuli have been studied using an entropy-based model and a failure machinery approach. The used tools include the fast Fourier transform and a spectral entropy analysis. The results indicate that the reaction times produced by the independently responding individuals to visual stimuli appear to be correlated. The spectral analysis and the entropy of the spectrum yield that there are features of similarity in the response times of each participant and among them. Furthermore, the analysis of the mistakes made by the participants during the reaction time experiments concluded that they follow a behavior which is consistent with the MTBF (Mean Time Between Failures) model, widely used in industry for the predictive diagnosis of electrical machines and equipment

The Schrödinger equation in the context of fluid mechanics

[ES] Se deriva un mapeo entre la ecuación de Schr¿odinger y la de Navier-Stokes, que generaliza el que propuso Madelung en 1926 con la ecuación de Euler. Dado que la mecánica de fluidos es el paradigma de teoría emergente, estos mapeos apoyan la interpretación de la mecánica cuántica como una teoría efectiva, emergente a partir de otra más fundamental. En el nuevo mapeo, además, el potencial cuántico se identifica con el término viscoso, en línea con recientes estudios que afirman que la cuanticidad tiene un origen disipativo.[EN] We derive a mapping between the Schro¿ dinger equation and the Navier-Stokes equation, which generalizes the one proposed by Madelung in 1926 with the Euler equation. Since ¿uid mechanics is the paradigm of an emergent theory, these maps support the interpretation of quantum mechanics as an effective theory, emerging from a more fundamental one. In the new mapping, moreover, the quantum potential is identi¿ed with the viscous term, in line with recent studies that claim that quantumness has a dissipative origin.J. Vazquez agradece a Manuel Monleón Pradas las referencias y discusiones sobre mecánica del medio continuo, y agradece la financiación al Programa de Becas de Movilidad Académica de la AUIP y al Programa de Ayudas de Investigación y Desarrollo de la UPV. D. Cabrera agradece la financiación del proyecto con Ref. FIS2014-51948-C2-1-P del Ministerio de Economía y Competitividad (España).Cabrera, D.; Fernández De Córdoba Castellá, PJ.; Isidro San Juan, JM.; Valdés Placeres, JM.; Vazquez Molina, J. (2016). La ecuación de Schrödinger en el contexto de la mecánica de fluidos. Revista Cubana de Fisica. 33(2):98-101. http://hdl.handle.net/10251/150048S9810133

Prognostic Value of Serum Paraprotein Response Kinetics in Patients With Newly Diagnosed Multiple Myeloma

Response kinetics is not well-established as a prognostic marker in multiple myeloma (MM). We developed a mathematical model to assess the prognostic value of serum monoclonal component (MC) response kinetics during 6 induction cycles in 373 newly diagnosed MM patients. The model calculated a resistance parameter that reflects the stagnation in the response after an initial descent, dividing the patients into two kinetics categories with significantly different progression-free survival (PFS). Introduction: Response kinetics is a well-established prognostic marker in acute lymphoblastic leukemia. The situation is not clear in multiple myeloma (MM) despite having a biomarker for response monitoring (monoclonal component [MC]). Materials and Methods: We developed a mathematical model to assess the prognostic value of serum MC response kinetics during 6 induction cycles, in 373 NDMM transplanted patients treated in the GEM2012Menos65 clinical trial. The model calculated a resistance parameter that reflects the stagnation in the response after an initial descent. Results: Two patient subgroups were defined based on low and high resistance, that respectively captured sensitive and refractory kinetics, with progression-free survival (PFS) at 5 years of 72% and 59% (HR 0.64, 95% CI 0.44-0.93; P =.02). Resistance significantly correlated with depth of response measured after consolidation (80.9% CR and 68.4% minimal residual disease negativity in patients with sensitive vs. 31% and 20% in those with refractory kinetics). Furthermore, it modulated the impact of reaching CR after consolidation; thus, within CR patients those with refractory kinetics had significantly shorter PFS than those with sensitive kinetics (median 54 months vs. NR; P =.02). Minimal residual disease negativity abrogated this effect. Our study also questions the benefit of rapid responders compared to late responders (5-year PFS 59.7% vs. 76.5%, respectively [P <.002]). Of note, 85% of patients considered as late responders were classified as having sensitive kinetics. Conclusion: This semi-mechanistic modeling of M-component kinetics could be of great value to identify patients at risk of early treatment failure, who may benefit from early rescue intervention strategies. (C) 2022 The Authors. Published by Elsevier Inc