Related papers: Markov models of macrosystems
In Boltzmannian statistical mechanics macro-states supervene on micro-states. This leads to a partitioning of the state space of a system into regions of macroscopically indistinguishable micro-states. The largest of these regions is…
Maximum entropy (MAXENT) method has a large number of applications in theoretical and applied machine learning, since it provides a convenient non-parametric tool for estimating unknown probabilities. The method is a major contribution of…
A statistical, path-dependent framework to describe time-dependent macroscopic theories using the Principle of Maximum Caliber is presented. By means of this procedure, it is possible to infer predictive non-equilibrium statistical…
This is a preliminary article stating and proving a new maximum entropy theorem. The entropies that we consider can be used as measures of biodiversity. In that context, the question is: for a given collection of species, which frequency…
In this study we apply the maximum entropy principle to derive the properly scaled velocity distribution function of Boltzmann equations for mixtures, which leads to a non-isothermal Maxwell-Stefan diffusion model. We also analyze the…
By specifying behaviour across multiple agents, social norms are a coordination approach to resolving social dilemmas. Decentralized and wide adoption can be achieved by norms whose prescription involves interpreting stochastic signals in…
The universal bound on specific entropy was originally inferred from black hole thermodynamics. We here show from classical thermodynamics alone that for a system at fixed volume or fixed pressure, the ratio of entropy to nonrelativistic…
We propose a macroscopic market making model \`a la Avellaneda-Stoikov, using continuous processes for orders instead of discrete point processes. The model intends to bridge the gap between market making and optimal execution problems,…
This paper characterizes differentiable and subgame Markov perfect equilibria in a continuous time intertemporal decision problem with non-constant discounting. Capturing the idea of non commitment by letting the commitment period being…
The field of complex networks studies a wide variety of interacting systems by representing them as networks. To understand their properties and mutual relations, the randomisation of network connections is a commonly used tool. However,…
In the paper, we introduce the maximum entropy estimator based on 2-dimensional empirical distribution of the observation sequence of hidden Markov model , when the sample size is big: in that case computing the maximum likelihood estimator…
Markov categories are a novel framework to describe and treat problems in probability and information theory. In this work we combine the categorical formalism with the traditional quantitative notions of entropy, mutual information, and…
Ill-posed inverse problems of the form y = X p where y is J-dimensional vector of a data, p is m-dimensional probability vector which cannot be measured directly and matrix X of observable variables is a known J,m matrix, J < m, are…
Stochastic network models play a central role across a wide range of scientific disciplines, and questions of statistical inference arise naturally in this context. In this paper we investigate goodness-of-fit and two-sample testing…
The Boltzmann and Gibbs approaches to statistical mechanics have very different definitions of equilibrium and entropy. The problems associated with this are discussed and it is suggested that they can be resolved, to produce a version of…
We demonstrate and characterize a first-principles approach to modeling the mass action dynamics of metabolism. Starting from a basic definition of entropy expressed as a multinomial probability density using Boltzmann probabilities with…
Maximum entropy principle (MEP) offers an effective and unbiased approach to inferring unknown probability distributions when faced with incomplete information, while neural networks provide the flexibility to learn complex distributions…
The possibility of reconciliation between canonical probability distributions obtained from the $q$-maximum entropy principle with predictions from the law of large numbers when empirical samples are held to the same constraints, is…
We introduce a comprehensive analytical benchmark, relying on Fokker-Planck formalism, to study microbial dynamics in presence of both biotic and abiotic forces. In equilibrium, we observe a balance between the two kinds of forces, leading…
We consider a system composed of a fixed number of particles with total energy smaller or equal to some prescribed value. The particles are non-interacting, indistinguishable and distributed over fixed number of energy levels. The energy…