{"title":"Universal and non-universal large deviations in critical systems","authors":"Ivan Balo, Bertrand Delamotte, Adam Rançon","doi":"arxiv-2409.01250","DOIUrl":"https://doi.org/arxiv-2409.01250","url":null,"abstract":"Rare events play a crucial role in understanding complex systems.\u0000Characterizing and analyzing them in scale-invariant situations is challenging\u0000due to strong correlations. In this work, we focus on characterizing the tails\u0000of probability distribution functions (PDFs) for these systems. Using a variety\u0000of methods, perturbation theory, functional renormalization group, hierarchical\u0000models, large $n$ limit, and Monte Carlo simulations, we investigate universal\u0000rare events of critical $O(n)$ systems. Additionally, we explore the crossover\u0000from universal to nonuniversal behavior in PDF tails, extending Cram'er's\u0000series to strongly correlated variables. Our findings highlight the universal\u0000and nonuniversal aspects of rare event statistics and challenge existing\u0000assumptions about power-law corrections to the leading stretched exponential\u0000decay in these tails.","PeriodicalId":501520,"journal":{"name":"arXiv - PHYS - Statistical Mechanics","volume":"57 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-09-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142196241","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Universal critical phase diagram using Gini index","authors":"Soumyaditya Das, Soumyajyoti Biswas","doi":"arxiv-2409.01453","DOIUrl":"https://doi.org/arxiv-2409.01453","url":null,"abstract":"The critical phase boundary of a system, in general, can depend on one or\u0000more parameters. We show that by calculating the Gini index ($g$) of any\u0000suitably defined response function of a system, the critical phase boundary can\u0000always be reduced to that of a single parameter, starting from $g=0$ and\u0000terminating at $g=g_f$, where $g_f$ is a universal number for a given\u0000universality class. We demonstrate the construction with analytical and\u0000numerical calculations of mean field transverse field Ising model and site\u0000diluted Ising model on the Bethe lattice, respectively. Both models have two\u0000parameter phase boundaries -- transverse field and Temperature for the first\u0000case and site dilution and temperature in the second case. Both can be reduced\u0000to single parameter transition points in terms of the Gini index. The method is\u0000generally applicable for any multi-parameter critical transition.","PeriodicalId":501520,"journal":{"name":"arXiv - PHYS - Statistical Mechanics","volume":"4 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-09-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142196239","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Microcanonical Free Cumulants in lattice systems","authors":"Felix Fritzsch, Tomaž Prosen, Silvia Pappalardi","doi":"arxiv-2409.01404","DOIUrl":"https://doi.org/arxiv-2409.01404","url":null,"abstract":"Recently, the full version of the Eigenstate Thermalization Hypothesis (ETH)\u0000has been systematized using Free Probability. In this paper, we present a\u0000detailed discussion of the Free Cumulants approach to many-body dynamics within\u0000the microcanonical ensemble. Differences between the later and canonical\u0000averages are known to manifest in the time-dependent fluctuations of extensive\u0000operators. Thus, the microcanonical ensemble is essential to extend the\u0000application of Free Probability to the broad class of extensive observables. We\u0000numerically demonstrate the validity of our approach in a non-integrable spin\u0000chain Hamiltonian for extensive observables at finite energy density. Our\u0000results confirm the full ETH properties, specifically the suppression of\u0000crossing contributions and the factorization of non-crossing ones, thus\u0000demonstrating that the microcanonical free cumulants encode ETH smooth\u0000correlations for both local and extensive observables.","PeriodicalId":501520,"journal":{"name":"arXiv - PHYS - Statistical Mechanics","volume":"24 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-09-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142196242","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Thermodynamic Langevin Equations","authors":"Amilcare Porporato, Salvatore Calabrese, Lamberto Rondoni","doi":"arxiv-2409.00811","DOIUrl":"https://doi.org/arxiv-2409.00811","url":null,"abstract":"The physical significance of the stochastic processes associated to the\u0000generalized Gibbs ensembles is scrutinized here with special attention to the\u0000thermodynamic fluctuations of small systems. The contact with the environment\u0000produces an interaction entropy, which controls the distribution of\u0000fluctuations and allows writing the generalized Gibbs ensembles for macrostates\u0000in potential form. This naturally yields exact nonlinear thermodynamic Langevin\u0000equations (TLEs) for such variables, with drift expressed in terms of entropic\u0000forces. The analysis of the canonical ensemble for an ideal monoatomic gas and\u0000the related TLEs show that introducing currents leads to nonequilibrium heat\u0000transfer conditions with interesting bounds on entropy production but with no\u0000obvious thermodynamic limit. For a colloidal particle under constant force, the\u0000TLEs for macroscopic variables are different from those for the microscopic\u0000position, typically used in the so-called stochastic thermodynamics; while TLEs\u0000are consistent with the fundamental equation obtained from the Hamiltonian,\u0000stochastic thermodynamics requires isothermal conditions and entropy\u0000proportional to position.","PeriodicalId":501520,"journal":{"name":"arXiv - PHYS - Statistical Mechanics","volume":"66 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142196260","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Percolation in semicontinuum geometries","authors":"Jasna C. K, V. Krishnadev, V. Sasidevan","doi":"arxiv-2409.00699","DOIUrl":"https://doi.org/arxiv-2409.00699","url":null,"abstract":"We study percolation problems of overlapping objects where the underlying\u0000geometry is such that in D-dimensions, a subset of the directions has a lattice\u0000structure, while the remaining directions have a continuum structure. The\u0000resulting semicontinuum problem describes the percolation of overlapping shapes\u0000in parallel layers or lanes with positional constraints for the placement of\u0000the objects along the discrete directions. Several semicontinuum percolation\u0000systems are analyzed like hypercuboids with a particular focus on 2D and 3D\u0000cases, disks, and parallelograms. Adapting the excluded volume arguments to the\u0000semicontinuum setting, we show that for the semicontinuum problem of\u0000hypercuboids, for fixed side-lengths of the hypercuboids along the directions\u0000in which a lattice structure is maintained, the percolation threshold is always\u0000independent of the side-lengths along the continuum directions. The result\u0000holds even when there is a distribution for the side-lengths along the\u0000continuum directions. Trends in the variation of the thresholds, as we vary the\u0000linear measure of the shapes along the continuum directions, are obtained for\u0000other semicontinuum models like disks and parallelograms in 2D. The results are\u0000compared with those of corresponding continuum and lattice models. For the 2D\u0000and 3D models considered, using Monte Carlo simulations, we verify the excluded\u0000volume predictions for the trends and numerical values of the percolation\u0000thresholds. Very good agreement is seen between the predicted numerical values\u0000and the simulation results. The semicontinuum setting also allows us to\u0000establish a connection between the percolation problem of overlapping shapes in\u00002D continuum and triangular lattice. We also verify that the isotropy of the\u0000threshold for anisotropic shapes and standard percolation universality class is\u0000maintained in the semicontinuum setting.","PeriodicalId":501520,"journal":{"name":"arXiv - PHYS - Statistical Mechanics","volume":"8 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142196261","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Exact moments for a run and tumble particle in a harmonic trap with a finite tumble time","authors":"Aoran Sun, Fangfu Ye, Rudolf Podgornik","doi":"arxiv-2409.00578","DOIUrl":"https://doi.org/arxiv-2409.00578","url":null,"abstract":"We study the problem of a run and tumble particle in a harmonic trap, with a\u0000finite run and tumble time, by a direct integration of the equation of motion.\u0000An exact 1D steady state distribution, diagram laws and a programmable Volterra\u0000difference equation are derived to calculate any order of moments in any other\u0000dimension, both for steady state as well as the Laplace transform in time for\u0000the intermediate states. We also use the moments to infer the distribution by\u0000considering a Gaussian quadrature for the corresponding measure, and from the\u0000scaling law of high order moments.","PeriodicalId":501520,"journal":{"name":"arXiv - PHYS - Statistical Mechanics","volume":"25 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142196265","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Models of heat transport with microscopic reversibility","authors":"Piero Olla","doi":"arxiv-2409.00430","DOIUrl":"https://doi.org/arxiv-2409.00430","url":null,"abstract":"The behavior of lattice models in which time reversibility is enforced at the\u0000level of trajectories (microscopic reversibility) is studied analytically.\u0000Conditions for ergodicity breaking are explored, and a few examples of systems\u0000characterized by an additional conserved quantity besides energy are presented.\u0000All the systems are characterized by ergodicity restoration when put in contact\u0000with a thermal bath, except for specific choices of the interactions between\u0000the atoms in the system and the bath. The study shows that the additional\u0000conserved quantities return to play a role in non-equilibrium conditions, with\u0000behaviors similar to those of some mesoscale systems, in which the transition\u0000rates satisfy detailed balance but not microscopic reversibility.","PeriodicalId":501520,"journal":{"name":"arXiv - PHYS - Statistical Mechanics","volume":"181 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-08-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142196262","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Oscillatory and dissipative dynamics of complex probability in non-equilibrium stochastic processes","authors":"Anwesha Chattopadhyay","doi":"arxiv-2409.00361","DOIUrl":"https://doi.org/arxiv-2409.00361","url":null,"abstract":"For a Markov and stationary stochastic process described by the well-known\u0000classical master equation, we introduce complex transition rates instead of\u0000real transition rates to study the pre-thermal oscillatory behaviour in complex\u0000probabilities. Further, for purely imaginary transition rates we obtain\u0000persistent infinitely long lived oscillations in complex probability whose\u0000nature depends on the dimensionality of the state space. We also take a peek\u0000into cases where we perturb the relaxation matrix for a dichotomous process\u0000with an oscillatory drive where the relative sign of the angular frequency of\u0000the drive decides whether there will be dissipation in the complex probability\u0000or not.","PeriodicalId":501520,"journal":{"name":"arXiv - PHYS - Statistical Mechanics","volume":"70 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-08-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142196263","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Petrus H. R. dos Anjos, Fernando A. Oliveira, David L. Azevedo
{"title":"Fractality in resistive circuits: The Fibonacci resistor networks","authors":"Petrus H. R. dos Anjos, Fernando A. Oliveira, David L. Azevedo","doi":"arxiv-2409.00229","DOIUrl":"https://doi.org/arxiv-2409.00229","url":null,"abstract":"We propose two new kinds of infinite resistor networks based on the Fibonacci\u0000sequence: a serial association of resistor sets connected in parallel (type 1)\u0000or a parallel association of resistor sets connected in series (type 2). We\u0000show that the sequence of the network's equivalent resistance converges\u0000uniformly in the parameter $alpha=frac{r_2}{r_1} in [0,+infty)$, where\u0000$r_1$ and $r_2$ are the first and second resistors in the network. We also show\u0000that these networks exhibit self-similarity and scale invariance, which mimics\u0000a self-similar fractal. We also provide some generalizations, including\u0000resistor networks based on high-order Fibonacci sequences and other recursive\u0000combinatorial sequences.","PeriodicalId":501520,"journal":{"name":"arXiv - PHYS - Statistical Mechanics","volume":"42 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-08-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142196264","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Frank Barrows, Jonathan Lin, Francesco Caravelli, Dante R. Chialvo
{"title":"Uncontrolled learning: co-design of neuromorphic hardware topology for neuromorphic algorithms","authors":"Frank Barrows, Jonathan Lin, Francesco Caravelli, Dante R. Chialvo","doi":"arxiv-2408.05183","DOIUrl":"https://doi.org/arxiv-2408.05183","url":null,"abstract":"Hardware-based neuromorphic computing remains an elusive goal with the\u0000potential to profoundly impact future technologies and deepen our understanding\u0000of emergent intelligence. The learning-from-mistakes algorithm is one of the\u0000few training algorithms inspired by the brain's simple learning rules,\u0000utilizing inhibition and pruning to demonstrate self-organized learning. Here\u0000we implement this algorithm in purely neuromorphic memristive hardware through\u0000a co-design process. This implementation requires evaluating hardware\u0000trade-offs and constraints. It has been shown that learning-from-mistakes\u0000successfully trains small networks to function as binary classifiers and\u0000perceptrons. However, without tailoring the hardware to the algorithm,\u0000performance decreases exponentially as the network size increases. When\u0000implementing neuromorphic algorithms on neuromorphic hardware, we investigate\u0000the trade-offs between depth, controllability, and capacity, the latter being\u0000the number of learnable patterns. We emphasize the significance of topology and\u0000the use of governing equations, demonstrating theoretical tools to aid in the\u0000co-design of neuromorphic hardware and algorithms. We provide quantitative\u0000techniques to evaluate the computational capacity of a neuromorphic device\u0000based on the measurements performed and the underlying circuit structure. This\u0000approach shows that breaking the symmetry of a neural network can increase both\u0000the controllability and average network capacity. By pruning the circuit,\u0000neuromorphic algorithms in all-memristive device circuits leverage stochastic\u0000resources to drive local contrast in network weights. Our combined experimental\u0000and simulation efforts explore the parameters that make a network suited for\u0000displaying emergent intelligence from simple rules.","PeriodicalId":501520,"journal":{"name":"arXiv - PHYS - Statistical Mechanics","volume":"11 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-08-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141943341","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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