Related papers: Towards a Geometry and Analysis for Bayesian Mecha…
Why is gauge symmetry so important in modern physics, given that one must eliminate it when interpreting what the theory represents? In this paper we discuss the sense in which gauge symmetry can be fruitfully applied to constrain the space…
We give a geometric description of variational principles in mechanics, with special attention to constrained systems. For the general case of nonholonomic constraints, a unified variational approach is given, and the equations of motion of…
We summarize the original formulation of the free energy principle, and highlight some technical issues. We discuss how these issues affect related results involving generalised coordinates and, where appropriate, mention consequences for…
We consider the problem of defining free energy and other thermodynamic functions when the entropy is given as a general function of the probablity distribution, including that for non extensive forms. We find that the free energy, which is…
Following our earlier work, we construct statistical discrete geometry by applying statistical mechanics to discrete (Regge) gravity. We propose a coarse-graining method for discrete geometry under the assumptions of atomism and background…
Dynamical systems of the gauge glass are investigated by the method of the gauge transformation.Both stochastic and deterministic dynamics are treated. Several exact relations are derived among dynamical quantities such as equilibrium and…
Quantum particles confined to surfaces in higher dimensional spaces are acted upon by forces that exist only as a result of the surface geometry and the quantum mechanical nature of the system. The dynamics are particularly rich when…
In contrast to the classical concept of a Carnot engine that alternates contact between heat baths of different temperatures, naturally occurring processes usually harvest energy from anisotropy, being exposed simultaneously to chemical and…
Transcription is a complex phenomenon that permits the conversion of genetic information into phenotype by means of an enzyme called RNA polymerase, which erratically moves along and scans the DNA template. We perform Bayesian inference…
In the context of the recently proposed formulation of quantum geometrodynamics in extended phase space we discuss the problem how the behavior of the Universe, initially managed by quantum laws, has become classical. In this version of…
The problem of extracting the work from a quantum-thermodynamic system driven by slowly varying external parameters is discussed. It is shown that there naturally emerges a gauge-theoretic structure. The field strength identically vanishes…
We study deterministic and quantum dynamics from a constructive "finite" point of view, since the introduction of a continuum, or other actual infinities in physics poses serious conceptual and technical difficulties, without any need for…
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…
People are well aware that, inherently, certain small-scale nonchaotic particle movements are not governed by thermodynamics. Usually, such phenomena are studied by kinetic theory and their energy properties are considered "trivial". In…
A statistical mechanism is proposed for symmetrization of an extra space. The conditions and rate of attainment of a symmetric configuration and, as a consequence, the appearance of gauge invariance in low-energy physics is discussed. It is…
Bayesian inference is a widely used statistical method. The free energy and generalization loss, which are used to estimate the accuracy of Bayesian inference, are known to be small in singular models that do not have a unique optimal…
In all areas of human knowledge, datasets are increasing in both size and complexity, creating the need for richer statistical models. This trend is also true for economic data, where high-dimensional and nonlinear/nonparametric inference…
We consider the Bayesian approach to the linear Gaussian inference problem of inferring the initial condition of a linear dynamical system from noisy output measurements taken after the initial time. In practical applications, the large…
Stochastic mechanics is regarded as a physical theory to explain quantum mechanics with classical terms such that some of the quantum mechanics paradoxes can be avoided. Here we propose a new variational principle to uncover more insights…
We consider a body immersed in a perfect gas, moving under the action of a constant force E along the x axis . We assume the gas to be described by the mean-field approximation and interacting elastically with the body, we study the…