2022/01/31 by Alexandre L. M. Levada, Levada, Alexandre L. M.
Computer Science · Mathematics · Physics and Astronomy · #53Z05 #60G60 #62B10 #62B11 #82B26 #94A15 #Computational Engineering #Computational Physics (physics.comp-ph) #FOS: Computer and information sciences #FOS: Physical sciences #Finance #G.3 #I.6 #Information Theory (cs.IT) #J.2 #Morphological variations and asymmetry #Statistical Mechanics (cond-mat.stat-mech) #Statistical Mechanics and Entropy #acm:53Z05 #acm:60G60 #acm:62B10 #acm:62B11 #acm:82B26 #acm:94A15 #and Science (cs.CE) #cond-mat.stat-mech #cs.CE #cs.IT #math.IT #msc:53Z05 #msc:60G60 #msc:62B10 #msc:62B11 #msc:82B26 #msc:94A15 #physics.comp-ph
paper · pdf · doi:10.48550/arxiv.2201.13215
5 pages, 5 figures. arXiv admin note: substantial text overlap with arXiv:2109.09204
arxiv created 2022/01/31 · openalex publication_date 2022/01/31 · arxiv updated 2022/02/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Random field models are mathematical structures used in the study of stochastic complex systems. In this paper, we compute the shape operator of Gaussian random field manifolds using the first and second fundamental forms (Fisher information matrices). Using Markov Chain Monte Carlo techniques, we simulate the dynamics of these random fields and compute the Gaussian curvature of the parametric space, analyzing how this quantity changes along phase transitions. During the simulation, we have observed an unexpected phenomenon that we called the curvature effect, which indicates that a highly asymmetric geometric deformation happens in the underlying parametric space when there are significant increase/decrease in the system's entropy. This asymmetric pattern relates to the emergence of hysteresis, leading to an intrinsic arrow of time along the dynamics.