2020/04/01 by Diego González, González, Diego, Sergio Davis +4
Physics and Astronomy · #Advanced Thermodynamics and Statistical Mechanics #Computational Physics (physics.comp-ph) #Data Analysis #FOS: Physical sciences #Scientific Research and Discoveries #Statistical Mechanics and Entropy #Statistics and Probability (physics.data-an)
paper · pdf · doi:10.48550/arxiv.2004.00624
openalex publication_date 2020/04/01 · openalex created_date 2022/07/26 · openalex updated_date 2026/07/28
A permanent challenge in physics and other disciplines is to solve partial\ndifferential equations, thereby a beneficial investigation is to continue\nsearching for new procedures to do it. In this Letter, a novel Monte-Carlo\nMetropolis framework is presented for solving the equations of motion in\nLagrangian systems. The implementation lies in sampling the paths space with a\nprobability functional obtained by using the maximum caliber principle. The\nmethodology was applied to the free particle and the harmonic oscillator\nproblems, where the numerically-averaged path obtained from the Monte-Carlo\nsimulation converges to the analytical solution from classical mechanics, in an\nanalogous way with a canonical system where energy is minimized by sampling the\nstate space and computing the average state for each system. Thus, we expect\nthat this procedure can be general enough to solve other differential equations\nin physics and to be a useful tool to calculate the time-dependent properties\nof dynamical systems in order to understand the non-equilibrium behavior of\nstatistical mechanical systems.\n