Statistical Physics

Stylized Facts and Their Microscopic Origins: Clustering, Persistence, and Stability in a 2D Ising Framework ArXiv ID: 2512.17925 “View on arXiv” Authors: Hernán Ezequiel Benítez, Claudio Oscar Dorso Abstract The analysis of financial markets using models inspired by statistical physics offers a fruitful approach to understand collective and extreme phenomena [“3, 14, 15”] In this paper, we present a study based on a 2D Ising network model where each spin represents an agent that interacts only with its immediate neighbors plus a term reated to the mean field [“1, 2”]. From this simple formulation, we analyze the formation of spin clusters, their temporal persistence, and the morphological evolution of the system as a function of temperature [“5, 19”]. Furthermore, we introduce the study of the quantity $1/2P\sum_{“i”}|S_{“i”}(t)+S_{“i”}(t+Δt)|$, which measures the absolute overlap between consecutive configurations and quantifies the degree of instantaneous correlation between system states. The results show that both the morphology and persistence of the clusters and the dynamics of the absolute sum can explain universal statistical properties observed in financial markets, known as stylized facts [“2, 12, 18”]: sharp peaks in returns, distributions with heavy tails, and zero autocorrelation. The critical structure of clusters and their reorganization over time thus provide a microscopic mechanism that gives rise to the intermittency and clustered volatility observed in prices [“2, 15”]. ...

Thermodynamic description of world GDP distribution over countries ArXiv ID: 2512.06420 “View on arXiv” Authors: Klaus M. Frahm, Dima L. Shepelyansky Abstract We apply the concept of Rayleigh-Jeans thermalization of classical fields for a description of the world Gross Domestic Product (GDP) distribution over countries. The thermalization appears due to a variety of interactions between countries with conservation of two integrals being total GDP and probability (norm). In such a case there is an emergence of Rayleigh-Jeans condensation at states with low GDP. This phenomenon has been studied theoretically and experimentally in multimode optical fibers and we argue that it is at the origin of emergence of poverty and oligarchic phases for GDP of countries. A similar phenomenon has been discussed recently in the framework of the Wealth Thermalization Hypothesis to explain the high inequality of wealth distribution in human society and companies at Stock Exchange markets. We show that the Rayleigh-Jeans thermalization well describes the GDP distribution during the last 50 years. ...

Critical Dynamics of Random Surfaces: Time Evolution of Area and Genus ArXiv ID: 2409.05547 “View on arXiv” Authors: Unknown Abstract Conformal field theories with central charge $c\le1$ on random surfaces have been extensively studied in the past. Here, this discussion is extended from their equilibrium distribution to their critical dynamics. This is motivated by the conjecture that these models describe the time evolution of certain social networks that are self-driven to a critical point. This paper focuses on the dynamics of the overall area and the genus of the surface. The time evolution of the area is shown to follow a Cox Ingersol Ross process. Planar surfaces shrink, while higher genus surfaces grow to a size of order of the inverse cosmological constant. The time evolution of the genus is argued to lead to two different phases, dominated by (i) planar surfaces, and (ii) ``foamy’’ surfaces, whose genus diverges. In phase (i), which exhibits critical phenomena, time variations of the order parameter are approximately t-distributed with 4 or more degrees of freedom. ...

Coarse graining correlation matrices according to macrostructures: Financial markets as a paradigm ArXiv ID: 2402.05364 “View on arXiv” Authors: Unknown Abstract We analyze correlation structures in financial markets by coarse graining the Pearson correlation matrices according to market sectors to obtain Guhr matrices using Guhr’s correlation method according to Ref. [“P. Rinn {"\it et. al.”}, Europhysics Letters 110, 68003 (2015)"]. We compare the results for the evolution of market states and the corresponding transition matrices with those obtained using Pearson correlation matrices. The behavior of market states is found to be similar for both the coarse grained and Pearson matrices. However, the number of relevant variables is reduced by orders of magnitude. ...

A closer look at the chemical potential of an ideal agent system ArXiv ID: 2401.09233 “View on arXiv” Authors: Unknown Abstract Models for spin systems known from statistical physics are used in econometrics in the form of agent-based models. Econophysics research in econometrics is increasingly developing general market models that describe exchange phenomena and use the chemical potential $μ$ known from physics in the context of particle number changes. In statistical physics, equations of state are known for the chemical potential, which take into account the respective model framework and the corresponding state variables. A simple transfer of these equations of state to problems in econophysics appears difficult. To the best of our knowledge, the equation of state for the chemical potential is currently missing even for the simplest conceivable model of an ideal agent system. In this paper, this research gap is closed and the equation of state for the chemical potential is derived from the econophysical model assumptions of the ideal agent system. An interpretation of the equation of state leads to fundamental relationships that could also have been guessed, but are shown here by the theory. ...

A standard form of master equations for general non-Markovian jump processes: the Laplace-space embedding framework and asymptotic solution ArXiv ID: 2312.05475 “View on arXiv” Authors: Unknown Abstract We present a standard form of master equations (ME) for general one-dimensional non-Markovian (history-dependent) jump processes, complemented by an asymptotic solution derived from an expanded system-size approach. The ME is obtained by developing a general Markovian embedding using a suitable set of auxiliary field variables. This Markovian embedding uses a Laplace-convolution operation applied to the velocity trajectory. We introduce an asymptotic method tailored for this ME standard, generalising the system-size expansion for these jump processes. Under specific stability conditions tied to a single noise source, upon coarse-graining, the Generalized Langevin Equation (GLE) emerges as a universal approximate model for point processes in the weak-coupling limit. This methodology offers a unified analytical toolset for general non-Markovian processes, reinforcing the universal applicability of the GLE founded in microdynamics and the principles of statistical physics. ...

An Empirical Analysis on Financial Markets: Insights from the Application of Statistical Physics ArXiv ID: 2308.14235 “View on arXiv” Authors: Unknown Abstract In this study, we introduce a physical model inspired by statistical physics for predicting price volatility and expected returns by leveraging Level 3 order book data. By drawing parallels between orders in the limit order book and particles in a physical system, we establish unique measures for the system’s kinetic energy and momentum as a way to comprehend and evaluate the state of limit order book. Our model goes beyond examining merely the top layers of the order book by introducing the concept of ‘active depth’, a computationally-efficient approach for identifying order book levels that have impact on price dynamics. We empirically demonstrate that our model outperforms the benchmarks of traditional approaches and machine learning algorithm. Our model provides a nuanced comprehension of market microstructure and produces more accurate forecasts on volatility and expected returns. By incorporating principles of statistical physics, this research offers valuable insights on understanding the behaviours of market participants and order book dynamics. ...

Detecting Financial Market Manipulation with Statistical Physics Tools ArXiv ID: 2308.08683 “View on arXiv” Authors: Unknown Abstract We take inspiration from statistical physics to develop a novel conceptual framework for the analysis of financial markets. We model the order book dynamics as a motion of particles and define the momentum measure of the system as a way to summarise and assess the state of the market. Our approach proves useful in capturing salient financial market phenomena: in particular, it helps detect the market manipulation activities called spoofing and layering. We apply our method to identify pathological order book behaviours during the flash crash of the LUNA cryptocurrency, uncovering widespread instances of spoofing and layering in the market. Furthermore, we establish that our technique outperforms the conventional Z-score-based anomaly detection method in identifying market manipulations across both LUNA and Bitcoin cryptocurrency markets. ...