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). 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Journal of Physics: Conference Series, 174, 012008. doi:10.1088/1742-6596/174/1/01200

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

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

Water content-water activity-glass transition temperature relationships of spray-dried borojó as related to changes in color and mechanical properties

The water content-water activity-glass transition temperature relationships of commercial spray-dried borojó powder, with and without maltodextrin, have been studied as related to changes in color and mechanical properties. The GAB and Gordon and Taylor models were well fitted to the sorption and glass transition data, respectively. The Boltzman equation adequately described the evolution of the mechanical parameter characterized in the samples with the difference between the experimental temperature and the glass transition temperature (T g) of the sample. The color of the samples showed a sigmoid change with water activity. The changes in the mechanical properties of borojó powder related to collapse development started when the sample moved to the rubbery state and began to be significant at about 10 °C above T g. The increase in the molecular mobility from this point on also favors browning reactions. Maltodextrin presence slows the caking kinetics but induces color changes to spray-dried borojó powderThe authors thank the Ministerio de Ciencia e Innovacion and the Fondo Europeo de Desarrollo regional (FEDER) for the financial support throughout Project AGL2010-22176 and the Project UTCH-NUFFIC (NPT/COL/073) for the grant given to LH Mosquera.Mosquera, LH.; Moraga Ballesteros, G.; Fernández De Córdoba Castellá, PJ.; Martínez Navarrete, N. (2011). Water content-water activity-glass transition temperature relationships of spray-dried borojó as related to changes in color and mechanical properties. Food Biophysics. 6(3):397-406. https://doi.org/10.1007/s11483-011-9215-2S39740663L.H. Mosquera, G. Moraga, N. Martínez-Navarrete, J Food Eng 9, 72 (2010). doi: 10.1016/j.jfoodeng.2009.09.017V. Truong, B.R. Bhandari, T. Howe, J Food Eng 71, 55 (2005). doi: 10.1016/j.jfoodeng.2004.10.017B. Bhandari, Glass transition in relation to stickiness during spray drying (Academic Sterling, London, 2001), p. 64Y. Roos, Phase transitions in foods (Academic, New York, 1995), p. 360P. Saragoni, J.M. Aguilera, P. Bouchon, Food Chem 104, 122 (2007). doi: 10.1016/j.foodchem.2007.11.066C.K. Pua, N. Sheikh Abd. Hamid, C.P. Tanm, H. Mirhosseini, R. Abd. Rahman, G. Rusul, J Food Eng 89, 419 (2008). doi: 10.1016/j.jfoodeng.2008.05.023V.R.N. Telis, N. Martínez-Navarrete, LWT Food Sci Technol 43, 744 (2010)L. Greenspan, J Res Natl Inst Stand 81, 89 (1977). IDS: DM875W.E.L. Spiess, W.R. Wolf, in Physical properties of foods, ed by F. Escher, B. Hallstrom, H.S. Mefert, W.E.L. Spiess, G. Woss. (Applied Sci, New York, 1983), p. 65C. Van den Berg, S. Bruin, in Water activity and its estimation in food systems: theoretical aspects, ed by L.B. Rockland, G.T. Stewart (Academic Press, London, 1981), p. 43M. Gordon, J.S. Taylor, J Appl Chem 2, 493 (1952). doi: 10.1002/jctb.5010020901GV.R.N. Telis, N. Martínez-Navarrete, Food Biophys 4, 83 (2009). doi: 10.1007/s11483-003-9104-0G. Moraga, N. Martínez-Navarrete, A. Chiralt, J Food Eng 62, 315 (2004). doi: 10.1016/S0260-8774(03)00245-0C.I. Beristain, E. Azuara, E.J. Vernon-Carter, J Food Sci 67, 211 (2002). IDS: 522JPB.R. Bandhari, R.W. Hartel, in Encapsulated and food powder, ed by C. Onwulata, R.P. Konstance (Marcel Dekker, New York, 2005), p. 216N. William, Estadística para Ingenieros y Científicos (MacGraw-Hill, Mexico, 2006), p. 120A.L. Gabas, V.R.N. Telis, P.J.A. Sobral, J. Telis-Romero, J Food Eng 82, 246 (2007). doi: 10.1016/j.jfoodeng.2007.02.029M.A. Silva, P.J.A. Sobral, T.G. Kieckbusch, J Food Eng 77, 426 (2006). doi: 10.1016/j.jfoodeng.2005.07.009MdK Haque, Y.H. Ross, Innov Food Sci Emerg Technol 7, 1–2 (2006). doi: 10.1016/j.ifset.2004.12.004J.M. Aguilera, J.M. del Valle, M. Karel, Trends Food Sci Technol 8, 149 (1995). doi: 10.1016/S0924-2244(00)89023H. Levine, L. Slade, Cryoletters 9, 21 (1988). IDS: M1923Y.H. Ross, J Food Eng 24, 339 (1995). doi: 10.1016/0260-8774(95)90050-LG. Barbosa-Canovas, E. Ortega-Rivas, P. Juliano, H. Yan, Food powders: physical properties, processing and functionality (Kluwer Academic/Plenum Publisher, New York, 2005), p. 372K.D. Foster, J.E. Bronlund, A.H.J. Paterson, J Food Eng 77, 997 (2006). doi: 10.1016/j.jfoodeng.2005.08.028E. Venir, M. Munari, A. Tonizzo, E.J. Maltini, Food Eng 81, 27 (2007). doi: 10.1016/j.jfoodeng.2006.10.004N.C. Acevedo, C. Schebor, P. Buera, J Food Eng 77, 1108 (2006). doi: 10.1016/j.jfoodeng.2005.08.045N.C. Acevedo, C. Schebor, P. Buera, Food Chem 108, 900 (2008). doi: 10.1016/j.foodchem.2007.11.057J. Ahmed, U.S. Shivhareb, P. Singhc, Food Chem 84, 605 (2004). doi: 10.1016/S0308-8146(03)00285-1L. Hang-Ing Ling, J. Birch, M. Lim, Int J Food Sci Technol 40, 921 (2005). doi: 10.1111/j.1365-2621.2005.0099

Improving parameter estimates obtained from thermal response tests: Effect of ambient air temperature variations

[EN] This paper presents a method of subtracting the effect of atmospheric conditions from thermal response test (TRT) estimates by using data on the ambient air temperature. The method assesses effective ground thermal conductivity within 10% of the mean value from the test, depending on the time interval chosen for the analysis, whereas the estimated value can vary by a third if energy losses outside the borehole are neglected. Evaluating the same test data using the finite line-source (FLS) model gives lower values for the ground thermal conductivity than for the infinite line-source (ILS) model, whether or not heat dissipation to ambient air is assumed.This paper has been supported by the European Union Commission under projects GROUND-MED FP7-ENERGY-2007-2-TREN-218895, 043340, and Geotrainet - IEE/07/581; the Spanish Ministry of Education and Science under projects "Modelado y simulacion de sistemas energeticos complejos" (Programa Ramon y Cajal 2005) and ENE2008-00599/CON; by the Government of Valencia under project GV/2008/292; and by PAID-06-09/2734.Bandos, T.; Montero Reguera, ÁE.; Fernández De Córdoba Castellá, PJ.; Urchueguía Schölzel, JF. (2011). Improving parameter estimates obtained from thermal response tests: Effect of ambient air temperature variations. Geothermics. 40(2):136-143. https://doi.org/10.1016/j.geothermics.2011.02.003S13614340

Use of thermal conductivity from thermal response test for estimating steady-state temperatures in rock and stratified soil near a line source of heat

This article addresses the influence of anisotropy of the ground on steady-state temperature in the surroundings of vertical borehole and effective thermal conductivity measured by a field thermal response test. This is a key parameter in the design of ground coupled heat pumps to heat and cool buildings. First, this article provides a brief overview of the current technique of estimating thermal conductivity from data obtained in a thermal response test based on predictions for temperature from a line source of heat in an isotropic ground. Then, the analytical solutions to the isotropic model for the ground are used to obtain the solutions to the anisotropic model for stratified medium. In addition, the article provides a new analytical exact solution for temperatures around a finite line source of heat penetrating anisotropic semi-infinite medium, in which the angle between the ground surface and the sedimentary strata is arbitrary. Approximate expressions for the temperature evolution during the test and for the steady-state temperature are presented. Such approximate expressions are also given for integral mean temperature for two special orientations of the strata. The limitations of the finite line source method in stratified medium and recommendations for layout of multiple vertical or horizontal ground coupled heat exchangers or waste canisters in repository rock are discussed. Copyright © 2011 American Society of Heating, Refrigerating and Air-Conditioning Engineers.This paper has been supported by the European Union Commission under project 043340, and Geotrainet-IEE/07/581; the Spanish Ministry of Education and Science under projects "Modelado y simulacion de sistemas energeticos complejos" (Programa Ramon y Cajal 2005) and ENE2008-00599/ CON; by the Government of Valencia under project GV/2008/292; and by PAID-06-09/2734.Bandos, T.; Montero Reguera, ÁE.; Fernández De Córdoba Castellá, PJ.; Urchueguía Schölzel, JF. (2011). Use of thermal conductivity from thermal response test for estimating steady-state temperatures in rock and stratified soil near a line source of heat. HVAC&R Research. 17(6):1030-1043. https://doi.org/10.1080/10789669.2011.625349S1030104317

Unisolvency for Multivariate Polynomial Interpolation in Coatmèlec Configurations of Nodes

A new and straightforward proof of the unisolvability of the problem of multivariate polynomial interpolation based on Coatmèlec configurations of nodes, a class of properly posed set of nodes defined by hyperplanes, is presented. The proof generalizes a previous one for the bivariate case and is based on a recursive reduction of the problem to simpler ones following the so-called Radon–Bézout process.The authors thank to Drs. Mariano Gasca and Juan I. Ramos for pointing us some references and for their useful comments which have greatly improved the presentation. The authors also thank a reviewer for pointing out a mistake in the original Proof of Lemma 5. The research reported in this paper was partially supported by Project MTM2010-19969 from the Ministerio de Ciencia e Innovacion of Spain and Grant PAID-06-09-2734 from the Universidad Politecnica de Valencia. M. A. G. M. acknowledges support from the Spanish Ministry of Science and Education (MEC), Fulbright Commission, and FECYT.García March, MÁ.; Gimenez Palomares, F.; Villatoro, FR.; Pérez Quiles, MJ.; Fernández De Córdoba Castellá, PJ. (2011). Unisolvency for Multivariate Polynomial Interpolation in Coatmèlec Configurations of Nodes. Applied Mathematics and Computation. 217(18):7427-7431. https://doi.org/10.1016/j.amc.2011.02.034S742774312171

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)

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

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