Maximum entropy for dynamic processes on networks

Noam Abadi; Franco Ruzzenenti

Home/Archive/arXiv

arXiv · 2504.04240

Maximum entropy for dynamic processes on networks

Noam Abadi·Franco Ruzzenenti

View original source ↗Read source document ↗Export metadata ↓

Abstract

Dynamic processes on networks are fundamental to understanding modern-day phenomena such as information diffusion and opinion polarization on the internet or epidemics spreading through society. However, such processes are notoriously difficult to study broadly as small changes in initial conditions, the process, or the network can lead to very different evolution trajectories. Here we apply the information-theoretic framework of maximum caliber to study the statistics of such systems analytically, focusing on processes that can be interpreted as driven by interactions between populations of different types of individuals in the network. We verify the dynamics deduced from maximum caliber by using simulations of different processes on different networks, introduce an approximation of the dynamics that significantly simplifies the problem, and show that the approximation can be used to recover well-established models of population dynamics that are typically not thought of as taking place on networks.

Explore related subjects

physics.soc-ph cond-mat.stat-mech physics.data-an

Keep this discovery

Explore connections, maps & timelines

BibTeX RIS

Noam Abadi, Franco Ruzzenenti. 2025-07-14. Maximum entropy for dynamic processes on networks. https://arxiv.org/abs/2504.04240

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

Quantifying the Dynamics of Innovation Abandonment Across Scientific, Technological, Commercial, and Pharmacological Domains

Despite the vast literature on the diffusion of innovations that impacts a broad range of disciplines, our understanding of the abandonment of innovations remains limited yet is essential for a deeper understanding of the innovation lifecycle. Here, we analyze four large-scale datasets that capture the temporal and structural patterns of innovation abandonment across scientific, technological, commercial, and pharmacological domains. The paper makes three primary contributions. First, across these diverse domains, we uncover one simple pattern of preferential abandonment, whereby the probability for individuals or organizations to abandon an innovation increases with time and correlates with the number of network neighbors who have abandoned the innovation. Second, we find that the presence of preferential abandonment fundamentally alters the way in which the underlying ecosystem breaks down, inducing a novel structural collapse in networked systems commonly perceived as robust against abandonments. Third, we derive an analytical framework to systematically understand the impact of preferential abandonment on network dynamics, pinpointing specific conditions where it may accelerate, decelerate, or have an identical effect compared to random abandonment, depending on the network topology. Together, these results deepen our quantitative understanding of the abandonment of innovation within networked social systems, with implications for the robustness and functioning of innovation communities. Overall, they demonstrate that the dynamics of innovation abandonment follow simple yet reproducible patterns, suggesting that the uncovered preferential abandonment may be a generic property of the innovation lifecycle.

physics.soc-ph↗

arXiv2026

Emotions as intrinsic colored noise in biological systems

The idea that emotions in biological systems are analogous to intrinsic colored noise is advanced and justified. A model describing the dynamics of operation of biological networks under the influence of colored noise is suggested. The agents of a biological network can be represented either by biological species, such as humans and animals, or by neurons of the brain, or by the nodes of a neural network. Operational actions, or decisions, in a biological noisy network are based not only on the evaluation of utility of alternatives, but also on the agents emotions. The model is probabilistic, with the choice of alternatives characterized by the related probabilities. At the initial step, the agents make decisions individually and then start exchanging information with each other and imitating the actions of other agents, thus forming a biological network of interacting agents. Numerical simulations are accomplished for a heterogeneous society consisting of three groups of agents, one group possessing long-range memory, the other group, short-range memory, and the third group of super-rational agents acting strictly on the basis of utility, being deprived of emotions. Dynamics of opinions in different groups can be smooth, oscillatory, or chaotic. Altogether, eight types of operation are found, depending on the dynamics of group decisions. Under strong imitation effect, there appears chaotic motion in the evolution of decision choice. It is shown how the Ellsberg paradox can be resolved and how the exchange of information influences the dynamics of this paradox.

physics.soc-ph↗

arXiv2026

Beyond expressiveness in pairwise and higher-order models

The debate over pairwise and higher-order models is often cast as a contest of expressive power, but this framing is misleading. A graph with arbitrary multivariate node functions can emulate the node-level dynamics of many hypergraph models, yet this does not erase the grouping information encoded by the hypergraph: it may simply be shifted from structure to dynamics. We distinguish four notions that are often conflated: structural projection, functional representability, statistical identifiability, and mechanistic adequacy. We show that the interaction order of a finite-state map is an invariant of the map itself, so an exact change of representation cannot reduce the underlying order of dependence. We then recast the comparison in terms of description length. At the unrestricted algorithmic level, a fixed compiler can move information between structure and rule with only constant overhead, so expressiveness alone does not privilege graphs or hypergraphs. Preferences arise only relative to explicit model classes, coding schemes, regularity assumptions, and data. This motivates an operational minimum-description-length criterion combining structural cost, rule cost conditional on structure, and model fit. For $M$ disjoint groups of size $k$, we show that the clique projection requires an edge list asymptotically $k-1$ times longer than the corresponding hyperedge list, making projection a more expensive encoding of the same grouping. Examples spanning diffusion, Boolean dynamics, ecological interactions, and ambiguous projections illustrate graph-preferred, hypergraph-preferred, and unresolved cases. The resulting position is symmetric: higher-order structure should not be inferred from phenomenology alone, but neither should graph-based emulation be taken as evidence that a graph is the most parsimonious or scientifically adequate description.

physics.soc-ph↗