Un vistazo a la mecánica estadística
Resumen
Este documento pretende introducir conceptos básicos de mecánica estadística en el equilibrio, y poner sobre la mesa la relación que existe entre los mundos microscópicos y macroscópicos. Se empieza con conceptos básicos de termodinámica. Para luego concluir con la colectividad estadística. El desarrollo de la teoría se basa en la presentación de ejemplos ilustrativos pero relevantes, que ayuden al lector a construir de manera natural los conceptos y proporcionen una motivación a la teoría en general. Además, se presentan simulaciones apoyadas por medio del lenguaje Python.
Citas
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Bernardin, C., Cardoso, P., Goncalves, P., y Scotta, S. (2020). Hydrodynamic limit for a boundary driven super-diffusive symmetric exclusion. arXiv preprint arXiv:2007.01621.
Bernardin, C., Goncalves, P., y Jiménez-Oviedo, B. (2019). Slow to fast infinitely extended reservoirs for the symmetric exclusion process with long jumps. Markov Processes And Related Fields.
Bernardin, C., Goncalves, P., y Jiménez-Oviedo, B. (2021). A microscopic model for a one parameter class of fractional laplacians with dirichlet boundary conditions. Archive for Rational Mechanics and Analysis, 239(1), 1–48.
Bernardin, C., y Jiménez-Oviedo, B. (2016). Fractional fick’s law for the boundary driven exclusion process with long jumps. Latin American Journal of Probability and Mathematical Statistics 14.
Bertini, L., De Sole, A., Gabrielli, D., Jona-Lasinio, G., y Landim, C. (2007). Stochastic interacting particle systems out of equilibrium. Journal of Statistical Mechanics: Theory and Experiment, 2007(07), P07014.
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Chung, K. L., y Zhong, K. (2001). A course in probability theory. Academic press.
Ciaburro, G. (2020). Hands-on simulation modeling with python: Develop simulation models to get accurate results and enhance decision-making processes. Packt Publishing Ltd.
Civitarese, O., y Gadella, M. (2020). Methods in statistical mechanics: A modern view (Vol. 974). Springer Nature.
Dobrow, R. P. (2016). Introduction to stochastic processes with R. John Wiley & Sons.
Feldman, R. M., y Valdez-Flores, C. (2010). Applied probability and stochastic
processes. Springer.
Friedli, S., y Velenik, Y. (2017). Statistical mechanics of lattice systems: a concrete mathematical introduction. Cambridge University Press.
Garanin, D. (2012). Statistical thermodynamics-fall 2009.
Goncalves, P., y Jiménez-Oviedo, B. (2019). Proceso de exclusión simple simétrico y la ecuación de calor. Revista Digital: Matemática, Educación e Internet, 19(2).
Goulet, J.-A. (2020). Probabilistic machine learning for civil engineers. MIT Press.
Gratton, J. (2003). Termodinámica e introducción a la mecánica estadística. Departamento de Física, Buenos Aires.
Guttmann, Y. M. (1999). The concept of probability in statistical physics. Cambridge University Press.
Jara, M. (2008). Hydrodynamic limit of particle systems with long jumps. arXiv preprint arXiv:0805.1326.
Jiménez-Oviedo, B., y Jiménez, J. R. (2021). Hydrostatic limit for the symmetric exclusion process with long jumps: Supper-diffusive case. Revista de Matemática: Teoría y Aplicaciones, 28(1), 79–94.
Jiménez-Oviedo, B., y Vavasseur, A. (2016). Hydrostatic limit and fick’s law for the symmetric exclusion with long jumps. En Meeting on particle systems and pde’s (pp. 81–104).
Kipnis, C., y Landim, C. (1998). Scaling limits of interacting particle systems
(Vol. 320). Springer Science & Business Media.
Krauth, W. (2010). Four lectures on computational statistical physics. Exact
Methods in Low-dimensional Statistical Physics and Quantum Computing: Lecture Notes of the Les Houches Summer School: Volume 89, July 2008, 127
Lange, K. (2003). Applied probability (Vol. 224). Springer.
Lavis, D. (2001). The concept of probability in statistical mechanics. En Frontiers of fundamental physics 4 (pp. 293–308). Springer.
Liggett, T. M. (1985). Interacting particle systems (Vol. 2). Springer.
Lim, C., y Nebus, J. (2007). Vorticity, statistical mechanics, and monte carlo simulation. Springer.
Malthe-Sorenssen, A., y Dysthe, D. (2017). Statistical and thermal physics using python. Department of Physics, University of Oslo, Norway.
Oviedo, B. J., y Jiménez, J. R. (2021). Hydrostatic limit for the symmetric exclusion process with long jumps: Supper-diffusive case. Revista de Matemática: Teoría y Aplicaciones, 28(1), 79–94.
Robbins, H. (1955). A remark on stirling’s formula. The American mathematical monthly, 62(1), 26–29.
Ross, S. M. (2020). Introduction to probability and statistics for engineers and scientists. Academic press.
Ruelle, D. (1999). Statistical mechanics: Rigorous results. World Scientific.
Simon, M. (2015). First principles of statistical mechanics.
Soni, J., y Goodman, R. (2017). A mind at play: how claude shannon invented the information age. Simon and Schuster.
Spitzer, F. (1991). Interaction of markov processes. En Random walks, brownian motion, and interacting particle systems (pp. 66–110). Springer.
Swendsen, R. (2020). An introduction to statistical mechanics and thermodynamics. Oxford University Press, USA.
Unpingco, J. (2016). Python for probability, statistics, and machine learning
(Vol. 1). Springer.
Viot, P. (2014). Numerical simulation in statistical physics lecture in master 2
“physics of complex systems” and “modeling, statistics and algorithms for
out-of-equilibrium systems. Laboratoire de Physique Theorique de la Matiere Condensee, Paris -2014.
Beale, P. D., y Pathria, R. (2011). Statistical mechanics. Elsevier Science.
Bernardin, C., Cardoso, P., Goncalves, P., y Scotta, S. (2020). Hydrodynamic limit for a boundary driven super-diffusive symmetric exclusion. arXiv preprint arXiv:2007.01621.
Bernardin, C., Goncalves, P., y Jiménez-Oviedo, B. (2019). Slow to fast infinitely extended reservoirs for the symmetric exclusion process with long jumps. Markov Processes And Related Fields.
Bernardin, C., Goncalves, P., y Jiménez-Oviedo, B. (2021). A microscopic model for a one parameter class of fractional laplacians with dirichlet boundary conditions. Archive for Rational Mechanics and Analysis, 239(1), 1–48.
Bernardin, C., y Jiménez-Oviedo, B. (2016). Fractional fick’s law for the boundary driven exclusion process with long jumps. Latin American Journal of Probability and Mathematical Statistics 14.
Bertini, L., De Sole, A., Gabrielli, D., Jona-Lasinio, G., y Landim, C. (2007). Stochastic interacting particle systems out of equilibrium. Journal of Statistical Mechanics: Theory and Experiment, 2007(07), P07014.
Bertsekas, D., y Tsitsiklis, J. N. (2008). Introduction to probability (Vol. 1). Athena Scientific.
Chung, K. L., y Zhong, K. (2001). A course in probability theory. Academic press.
Ciaburro, G. (2020). Hands-on simulation modeling with python: Develop simulation models to get accurate results and enhance decision-making processes. Packt Publishing Ltd.
Civitarese, O., y Gadella, M. (2020). Methods in statistical mechanics: A modern view (Vol. 974). Springer Nature.
Dobrow, R. P. (2016). Introduction to stochastic processes with R. John Wiley & Sons.
Feldman, R. M., y Valdez-Flores, C. (2010). Applied probability and stochastic
processes. Springer.
Friedli, S., y Velenik, Y. (2017). Statistical mechanics of lattice systems: a concrete mathematical introduction. Cambridge University Press.
Garanin, D. (2012). Statistical thermodynamics-fall 2009.
Goncalves, P., y Jiménez-Oviedo, B. (2019). Proceso de exclusión simple simétrico y la ecuación de calor. Revista Digital: Matemática, Educación e Internet, 19(2).
Goulet, J.-A. (2020). Probabilistic machine learning for civil engineers. MIT Press.
Gratton, J. (2003). Termodinámica e introducción a la mecánica estadística. Departamento de Física, Buenos Aires.
Guttmann, Y. M. (1999). The concept of probability in statistical physics. Cambridge University Press.
Jara, M. (2008). Hydrodynamic limit of particle systems with long jumps. arXiv preprint arXiv:0805.1326.
Jiménez-Oviedo, B., y Jiménez, J. R. (2021). Hydrostatic limit for the symmetric exclusion process with long jumps: Supper-diffusive case. Revista de Matemática: Teoría y Aplicaciones, 28(1), 79–94.
Jiménez-Oviedo, B., y Vavasseur, A. (2016). Hydrostatic limit and fick’s law for the symmetric exclusion with long jumps. En Meeting on particle systems and pde’s (pp. 81–104).
Kipnis, C., y Landim, C. (1998). Scaling limits of interacting particle systems
(Vol. 320). Springer Science & Business Media.
Krauth, W. (2010). Four lectures on computational statistical physics. Exact
Methods in Low-dimensional Statistical Physics and Quantum Computing: Lecture Notes of the Les Houches Summer School: Volume 89, July 2008, 127
Lange, K. (2003). Applied probability (Vol. 224). Springer.
Lavis, D. (2001). The concept of probability in statistical mechanics. En Frontiers of fundamental physics 4 (pp. 293–308). Springer.
Liggett, T. M. (1985). Interacting particle systems (Vol. 2). Springer.
Lim, C., y Nebus, J. (2007). Vorticity, statistical mechanics, and monte carlo simulation. Springer.
Malthe-Sorenssen, A., y Dysthe, D. (2017). Statistical and thermal physics using python. Department of Physics, University of Oslo, Norway.
Oviedo, B. J., y Jiménez, J. R. (2021). Hydrostatic limit for the symmetric exclusion process with long jumps: Supper-diffusive case. Revista de Matemática: Teoría y Aplicaciones, 28(1), 79–94.
Robbins, H. (1955). A remark on stirling’s formula. The American mathematical monthly, 62(1), 26–29.
Ross, S. M. (2020). Introduction to probability and statistics for engineers and scientists. Academic press.
Ruelle, D. (1999). Statistical mechanics: Rigorous results. World Scientific.
Simon, M. (2015). First principles of statistical mechanics.
Soni, J., y Goodman, R. (2017). A mind at play: how claude shannon invented the information age. Simon and Schuster.
Spitzer, F. (1991). Interaction of markov processes. En Random walks, brownian motion, and interacting particle systems (pp. 66–110). Springer.
Swendsen, R. (2020). An introduction to statistical mechanics and thermodynamics. Oxford University Press, USA.
Unpingco, J. (2016). Python for probability, statistics, and machine learning
(Vol. 1). Springer.
Viot, P. (2014). Numerical simulation in statistical physics lecture in master 2
“physics of complex systems” and “modeling, statistics and algorithms for
out-of-equilibrium systems. Laboratoire de Physique Theorique de la Matiere Condensee, Paris -2014.
