Related papers: Towards a Geometry and Analysis for Bayesian Mecha…
Ergodicity, this is to say, dynamics whose time averages coincide with ensemble averages, naturally leads to Boltzmann-Gibbs (BG) statistical mechanics, hence to standard thermodynamics. This formalism has been at the basis of an enormous…
Symbolic dynamics has proven to be an invaluable tool in analyzing the mechanisms that lead to unpredictability and random behavior in nonlinear dynamical systems. Surprisingly, a discrete partition of continuous state space can produce a…
Many high-dimensional statistical inference problems are believed to possess inherent computational hardness. Various frameworks have been proposed to give rigorous evidence for such hardness, including lower bounds against restricted…
In this second article, we show a simple use of the Ignorance as defined in "Jaynes & Shannon's Constrained Ignorance and Surprise". By giving an example about the journey of a person, we believe to show some simple, obvious but…
The paper analyzes the probability distribution of the occupancy numbers and the entropy of a system at the equilibrium composed by an arbitrary number of non-interacting bosons. The probability distribution is derived both by tracing out…
The set of solutions inferred by the generic maximum entropy (MaxEnt) or maximum relative entropy (MaxREnt) principles of Jaynes - considered as a function of the moment constraints or their conjugate Lagrangian multipliers - is endowed…
In this paper we present a self-contained macroscopic description of diffusive systems interacting with boundary reservoirs and under the action of external fields. The approach is based on simple postulates which are suggested by a wide…
Kinetic constraints are generally expected to slow down dynamics in many-body systems, obstructing or even completely suppressing transport of conserved charges. Here, we show how gauge theories can defy this wisdom by yielding constrained…
Extremal principles are fundamental in our interpretation of phenomena in nature. One of the best known examples is the second law of thermodynamics, governing most physical and chemical systems and stating the continuous increase of…
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…
The aim of this work is to show that particle mechanics, both classical and quantum, Hamiltonian and Lagrangian, can be derived from few simple physical assumptions. Assuming deterministic and reversible time evolution will give us a…
This is the first of a series of papers in which a new formulation of quantum theory is developed for totally constrained systems, that is, canonical systems in which the hamiltonian is written as a linear combination of constraints…
The dynamical systems invariant under gauge transformations with higher order time derivatives of the gauge parameter are considered from the Hamiltonian point of view. We investigate the consequences of the basic requirements that the…
Dynamic Bayesian networks have been well explored in the literature as discrete-time models: however, their continuous-time extensions have seen comparatively little attention. In this paper, we propose the first constraint-based algorithm…
The gauge symmetries of a general dynamical system can be systematically obtained following either a Hamiltonean or a Lagrangean approach. In the former case, these symmetries are generated, according to Dirac's conjecture, by the first…
We develop Hamiltonian mechanics on Aristotelian manifolds, which lack local boost symmetry and admit absolute time and space structures. We construct invariant phase space dynamics, define free Hamiltonians, and establish a generalized…
Recovering dynamical equations from observed noisy data is the central challenge of system identification. We develop a statistical mechanics approach to analyze sparse equation discovery algorithms, which typically balance data fit and…
The aim of this work is to study the geometry underlying mechanics and its application to describe autonomous and nonautonomous conservative dynamical systems of different types; as well as dissipative dynamical systems. We use different…
We study glassy dynamics using a simulation of three soft Brownian particles confined to a two-dimensional circular region. If the circular region is large, the disks freely rearrange, but rearrangements are rarer for smaller system sizes.…
The microcanonical statistical mechanics of a set of self-gravitating particles is analyzed in mean-field approach. In order to deal with an upper bounded entropy functional, a softened gravitational potential is used. The softening is…