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We consider quantum systems which interact strongly with a rapidly varying environment and derive a Schrodinger-like equation which describes the time evolution of the average wave function. We show that the corresponding Hamiltonian can be…
Ferromagnetic models are harmonic oscillators in statistical mechanics. Beyond their original scope in tackling phase transition and symmetry breaking in theoretical physics, they are nowadays experiencing a renewal applicative interest as…
A broad set of empirical phenomenon in the study of social, economic and machine behaviour can be modelled as complex systems with averaging dynamics. However many of these models naturally result in consensus or consensus-like outcomes. In…
This paper analyzes the relationships between demographic and state-based evolutionary games and Hamilton's rule. It is shown that the classical Hamilton's rule (counterfactual method), combined with demographic payoffs, leads to easily…
Experiments in predator-prey systems show the emergence of long-term cycles. Deterministic model typically fails in capturing these behaviors, which emerge from the microscopic interplay of individual based dynamics and stochastic effects.…
A quantitative model of concurrent interaction is introduced. The basic objects are linear combinations of partial order relations, acted upon by a group of permutations that represents potential non-determinism in synchronisation. This…
An agent-based model for firms' dynamics is developed. The model consists of firm agents with identical characteristic parameters and a bank agent. Dynamics of those agents is described by their balance sheets. Each firm tries to maximize…
We study systems of interacting reinforced stochastic processes, where agents' decisions evolve under reinforcement, network-mediated interactions, and environmental influences. In competitive environments with irreducible networks, we…
We consider a macroscopic quantum system such as a qubit, interacting with a bath of fermions as in the Fr\"ohlich polaron model. The interaction Hamiltonian is thus linear in the macroscopic system variable, and bilinear in the fermions.…
Bayesian mechanics provides a framework that addresses dynamical systems that can be conceptualised as Bayesian inference. However, elucidating the requisite generative models is essential for empirical applications to realistic…
The first step in the counting operator analysis of the spectrum of any model Hamiltonian H is the choice of a Hermitean operator M in such a way that the third commutator with H is proportional to the first commutator. Next one calculates…
We introduce and study a model of an interacting population of agents who collaborate in groups which compete for limited resources. Groups are formed by random matching agents and their worth is determined by the sum of the efforts…
Dynamic properties of fermionic systems, like contollability, reachability, and simulability, are investigated in a general Lie-theoretical frame for quantum systems theory. Observing the parity superselection rule, we treat the fully…
We investigate how reinforcement learning agents can learn to cooperate. Drawing inspiration from human societies, in which successful coordination of many individuals is often facilitated by hierarchical organisation, we introduce Feudal…
The emergence of labor division in multi-agent system is analyzed by the method of statistical physics. Considering a system consists of N homogeneous agents. Their behaviors are determined by the returns from their production. Using the…
This paper studies a particular class of higher order conformally invariant dif- ferential operators and related integral operators acting on functions taking values in particular finite dimensional irreducible representations of the Spin…
Agent-based models provide a constructive approach to studying emergent dynamics in life-like systems composed of interacting, adaptive agents. Financial markets serve as a canonical example of such systems, where collective price dynamics…
This paper presents a model of capital accumulation for a large number of heterogenous producer-consumers in an exchange space in which interactions depend on agents' positions. Each agent is described by his production, consumption, stock…
Prediction and optimisation of a wheel loader's dynamic behaviour is a challenge due to tightly coupled, non-linear subsystems of different technical domains. Furthermore, a simulation regarding performance, efficiency, and operability…
Estimating intervention effects in dynamical systems is crucial for outcome optimization. In medicine, such interventions arise in physiological regulation (e.g., cardiovascular system under fluid administration) and pharmacokinetics, among…