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We establish three partial differential equation models describing the thermodynamics of the fluid, by combining the energetic variational approach, appropriate constitutive relations, and classical thermodynamics laws. What is more, by…
Competitive balance model has been proposed as an extension to the balance model to address the conflict of interests in signed networks arXiv:2001.04664 . In this model two different paradigms compete with each other due to the competitive…
In this paper we consider first order differential models of collective behaviors of groups of agents based on the mass conservation equation. Models are formulated taking the spatial distribution of the agents as the main unknown,…
The limit of small entropy production is reached in relaxing systems long after preparation, and in stationary driven systems in the limit of small driving power. Surprisingly, for extended systems this limit is not in general the…
We derive a class of macroscopic differential equations that describe collective adaptation, starting from a discrete-time stochastic microscopic model. The behavior of each agent is a dynamic balance between adaptation that locally…
The \$-Game was recently introduced as an extension of the Minority Game. In this paper we compare this model with the well know Minority Game and the Majority Game models. Due to the inter-temporal nature of the market payoff, we introduce…
The game dynamical equations are derived from Boltzmann-like equations for individual pair interactions by assuming a certain kind of imitation behavior, the so-called proportional imitation rule. They can be extended to a stochastic…
We discuss a simple version of the Minority Game (MG) in which agents hold only one strategy each, but in which their capitals evolve dynamically according to their success and in which the total trading volume varies in time accordingly.…
Many complex adaptive systems contain a large diversity of specialized components. The specialization at the level of the microscopic degrees of freedom, and diversity at the level of the system as a whole are phenomena that appear during…
Our previous study [1] has demonstrated that the gauge theory is a proper framework for characterizing the local temporal and spatial interactions in inhomogeneous elastic media. However, in that study temporal interactions were interpreted…
We discuss what the presently collected data tell us about the mechanism of multifragmentation by comparing the results of two different models, which assume or show an opposite reaction scenario, with the recent high statistics $4\pi$…
It is argued the the idea of a single temperature-like variable, introduced in [1], which enters a generalized second law for Markovian open system in non-equilibrium environment is not sufficient for a consistent and useful thermodynamic…
We present detailed numerical results for a modified form of the so-called Minority Game, which provides a simplified model of a competitive market. Each agent has a limited set of strategies, and competes to be in a minority. An…
The Minority Game is a simple yet highly non-trivial agent-based model for a complex adaptive system. Despite its importance, a quantitative explanation of the game's fluctuations which applies over the entire parameter range of interest…
We review the recent approaches to modelling financial markets based on multi-agent systems. After a brief summary of the basic stylised facts observed in real-market time-series we discuss some simple agent-based systems which are…
Collective intelligence emerges across biological, physical, and artificial systems without central coordination, yet a unifying principle governing such behaviour remains elusive. The Free Energy Principle explains how individual agents…
The new excluded volume hadron gas model by Singh et al. [1-7] is critically discussed. We demonstrate that in this model the results obtained from relations between thermodynamical quantities disagree with the corresponding results…
Evolutionary game theory has impacted many fields of research by providing a mathematical framework for studying the evolution and maintenance of social and moral behaviors. This success is owed in large part to the demonstration that the…
A stochastic model for behavioral changes by imitative pair interactions of individuals is developed. `Microscopic' assumptions on the specific form of the imitative processes lead to a stochastic version of the game dynamical equations.…
A mathematical model for behavioral changes by pair interactions (i.e. due to direct contact) of individuals is developed. Three kinds of pair interactions can be distinguished: Imitative processes, avoidance processes, and compromising…