Related papers: Markov Blanket Density and Free Energy Minimizatio…
Two known results on the relationship between conditional and unconditional independence are obtained as a consequence of the main result of this paper, a theorem that uses independence of Markov kernels to obtain a minimal condition which…
The fundamental concepts underlying in Markov networks are the conditional independence and the set of rules called Markov properties that translates conditional independence constraints into graphs. In this article we introduce the concept…
Properties of the free energy landscape in phase space of a dense hard sphere system characterized by a discretized free energy functional of the Ramakrishnan-Yussouff form are investigated numerically. A considerable number of glassy local…
The gain of free energy upon unmixing is determined via application of Markov state modeling (MSM), using an Ising model with a fixed number of up- and down-spins. MSM yields reasonable estimates of the free energies. However, a closer look…
We study a class of non-equilibrium quasi-stationary states for a Markov system interacting with two different thermal baths. We show that the work done under a slow, external change of parameters admits a potential, i.e., the free energy.…
The consistency across scales of a recently developed mathematical thermodynamic structure, between a continuous stochastic nonlinear dynamical system (diffusion process with Langevin or Fokker-Planck equations) and its emergent discrete,…
The goal of these lecture notes is to review the problem of free energy minimization as a unified framework underlying the definition of maximum entropy modelling, generalized Bayesian inference, learning with latent variables, statistical…
We develop a model free energy from an expansion that basically includes graphs without loops. From this calculation, we derive the temperature dependence of the density (or specific volume), the typical time scale of the…
This paper discusses the free energy of complex dislocation microstructures, which is a fundamental property of continuum plasticity. In the past, multiple models of the self energy of dislocations have been proposed in the literature that…
In the setting of continuum elasticity, phase transformations involving martensitic variants are modeled by a free energy density function that is non-convex in strain space. Here, we adopt an existing mathematical model in which we…
We define a characteristic energy density based on the measurement of the two first moments of the extrinsic injected power smoothed over time. Using the stationarity, we show that this definition characterizes an energy per degrees freedom…
This work extends the results of the recently developed theory of a rather complete thermodynamic formalism for discrete-state, continuous-time Markov processes with and without detailed balance. We aim at investigating the question that…
The power spectral density of an observable quantifies the amount of fluctuations at a given frequency and can reveal the influence of different timescales on the observable's dynamics. Here, we show that the spectral density in a…
A fermion ground state energy functional is set up in terms of particle density, relative pair density, and kinetic energy tensor density. It satisfies a minimum principle if constrained by a complete set of compatibility conditions. A…
We present a model-free data-driven inference method that enables inferences on system outcomes to be derived directly from empirical data without the need for intervening modeling of any type, be it modeling of a material law or modeling…
We formulate the computational processes of perception in the framework of the principle of least action by postulating the theoretical action as a time integral of the free energy in the brain sciences. The free energy principle is…
A set of variables is the Markov blanket of a random variable if it contains all the information needed for predicting the variable. If the blanket cannot be reduced without losing useful information, it is called a Markov boundary.…
Conditional independence and Markov properties are powerful tools allowing expression of multidimensional probability distributions by means of low-dimensional ones. As multidimensional possibilistic models have been studied for several…
Nucleation phenomena are ubiquitous in nature and the presence of impurities in every real and experimental system is unavoidable. Yet numerical studies of nucleation are nearly always conducted for entirely pure systems. We have studied…
We study notions of robustness of Markov kernels and probability distribution of a system that is described by $n$ input random variables and one output random variable. Markov kernels can be expanded in a series of potentials that allow to…