A unifying framework for mean-field theories of asymmetric kinetic Ising systems

Abstract

Kinetic Ising models are powerful tools for studying the non-equilibrium dynamics of complex systems. As their behavior is not tractable for large networks, many mean-field methods have been proposed for their analysis, each based on unique assumptions about the system's temporal evolution. This disparity of approaches makes it challenging to systematically advance mean-field methods beyond previous contributions. Here, we propose a unifying framework for mean-field theories of asymmetric kinetic Ising systems from an information geometry perspective. The framework is built on Plefka expansions of a system around a simplified model obtained by an orthogonal projection to a sub-manifold of tractable probability distributions. This view not only unifies previous methods but also allows us to develop novel methods that, in contrast with traditional approaches, preserve the system's correlations. We show that these new methods can outperform previous ones in predicting and assessing network properties near maximally fluctuating regimes.

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• Dynamical phase transitions in the nonreciprocal Ising model
• Broken detailed balance and entropy production in directed networks
• Controlled asymmetric Ising model implemented with parametric micromechanical oscillators
• Lattice physics approaches for neural networks
• Decomposing Thermodynamic Dissipation of Linear Langevin Systems via Oscillatory Modes and Its Application to Neural Dynamics
• Inferring entropy production in many-body systems using nonequilibrium maximum entropy
• State-space kinetic Ising model reveals task-dependent entropy flow in sparsely active nonequilibrium neuronal dynamics
• Information-geometric structure for chemical thermodynamics: An explicit construction of dual affine coordinates
• Solving the Kinetic Ising Model with Non-Reciprocity
• Effective Hamiltonian approach to kinetic Ising models: Application to an infinitely long-range Husimi-Temperley model
• Inference in neural networks using conditional mean-field methods