Related papers: Some interesting observations on the free energy p…
We use parameterized post-Friedmann (PPF) description for dark energy and apply ellipsoidal nested sampling to perform the Bayesian model selection method on different time-dependent dark energy models using a combination of $Planck$ and…
We use the light front ``machinery'' to study the behavior of a relativistic free particle and obtain the quantum commutation relations from the classical Poisson brackets. We argue that their usual projection onto the light-front…
The derivation of key equations for the variational Bayes approach is well-known in certain circles. However, translating the fundamental derivations (e.g., as found in Beal's work) to Friston's notation is somewhat delicate. Further, the…
We develop a novel data-driven approach to the inverse problem of classical statistical mechanics: given experimental data on the collective motion of a classical many-body system, how does one characterise the free energy landscape of that…
A phenomenological approach is presented that allows one to model, and thereby interpret, photoemission spectra of strongly correlated electron systems. A simple analytical formula for the self-energy is proposed. This self-energy describes…
The introduction of loopy belief propagation (LBP) revitalized the application of graphical models in many domains. Many recent works present improvements on the basic LBP algorithm in an attempt to overcome convergence and local optima…
A family of fast sampling methods is introduced here for molecular simulations of systems having rugged free energy landscapes. The methods represent a generalization of a strategy consisting of adjusting a model for the free energy as a…
The interacting quantum Bose gas is a random ensemble of many Brownian bridges (cycles) of various lengths with interactions between any pair of legs of the cycles. It is one of the standard mathematical models in which a proof for the…
Active inference, a corollary of the free energy principle, is a formal way of describing the behavior of certain kinds of random dynamical systems that have the appearance of sentience. In this chapter, we describe how active inference…
We consider $N$ bosons in a box in $\mathbb {R}^d$ with volume $N/\rho$ under the influence of a mutually repellent pair potential. The particle density $\rho\in (0,\infty)$ is kept fixed. Our main result is the identification of the…
Established idea-sets don't update seamlessly. The tension between new and old views of nature is e.g. documented in Galileo's dialogs and now present in many fields. However the science of Bayesian model-selection has made recent strides…
We present a method for determining the free energy of coexisting states from irreversible work measurements. Our approach is based on a fluctuation relation that is valid for dissipative transformations in partially equilibrated systems.…
Fast and accurate evaluation of free energy has broad applications from drug design to material engineering. Computing the absolute free energy is of particular interest since it allows the assessment of the relative stability between…
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.…
For classical discrete systems under constant composition typically refferred to substitutional alloys, we propose calculation method of Helmholtz free energy based on a set of special microscopic states. The advantage of the method is that…
Physics and economics are two disciplines that share the common challenge of linking microscopic and macroscopic behaviors. However, while physics is based on collective dynamics, economics is based on individual choices. This conceptual…
This paper develops a Bayesian mechanics for adaptive systems. Firstly, we model the interface between a system and its environment with a Markov blanket. This affords conditions under which states internal to the blanket encode information…
We consider the interacting Bose gas in the thermodynamic limit in a large box in $\R^d$ at positive temperature $1/\beta\in(0,\infty)$ with particle density $\sim\rho\in(0,\infty)$. We follow a path-integral approach and adopt from \cite…
One may impose to a system with spontaneous broken symmetry, boundary conditions which correspond to different pure states at two ends of a sample. For a discrete Ising-like broken symmetry, boundary conditions with opposite spins in two…
Thermodynamics of the XXX Heisenberg model is studied. The trace of the Boltzmann weight with respect to the Hilbert space is taken in the thermodynamic limit with the number of up-spins being fixed. The expression of the trace gives an…