Related papers: Relativistic Hamiltonian as an emergent structure …
In classical probability theory, the convergence of empirical frequencies to theoretical probabilities: as captured by the Law of Large Numbers (LLN): is treated as axiomatic and emergent from statistical assumptions such as independence…
In this paper, we investigate the asymptotic stability of finite-dimensional stochastic integrable Hamiltonian systems via information entropy. Specifically, we establish the asymptotic vanishing of Shannon entropy difference (with…
The method of Maximum (relative) Entropy (ME) is used to translate the information contained in the known form of the likelihood into a prior distribution for Bayesian inference. The argument is guided by intuition gained from the…
Information geometry is an emergent branch of probability theory that consists of assigning a Riemannian differential geometry structure to the space of probability distributions. We present an information geometric investigation of gases…
We investigate the effect of different metrizations of probability spaces on the information geometric complexity of entropic motion on curved statistical manifolds. Specifically, we provide a comparative analysis based upon Riemannian…
Considerations on the complementary time-dependent coordinate transformations emboding Lorentz transformation (LT) show that the relativistic energy-momentum relationship, implicitly the relativistic mass and energy, do not depend on the…
Assuming the minimal time to send a bit of information in the Einstein clock synchronization of the two clocks located at different positions, we introduce the extended metric to the information space. This modification of relativity…
The relativistic hydrodynamic model is applied to describe the expansion of the dense matter formed in relativistic heavy-ion collisions. The hydrodynamic expansion of the fluid, supplemented with the statistical emission of hadrons at…
The general framework of entropic dynamics is used to formulate a relational quantum dynamics. The main new idea is to use tools of information geometry to develop an entropic measure of the mismatch between successive configurations of a…
We explain the ubiquity and extremely slow evolution of non gaussian out-of-equilibrium distributions for the Hamiltonian Mean-Field model, by means of traditional kinetic theory. Deriving the Fokker-Planck equation for a test particle, one…
We propose a unified theoretical framework for quantifying spatio-temporal interactions in a stochastic dynamical system based on information geometry. In the proposed framework, the degree of interactions is quantified by the divergence…
Prompted by the realisation that the statistical entropy of an ideal gas in the micro-canonical ensemble should not fluctuate or change over time, the meaning of the H-theorem is re-interpreted from the perspective of information theory in…
It is known that statistical model selection as well as identification of dynamical equations from available data are both very challenging tasks. Physical systems behave according to their underlying dynamical equations which, in turn, can…
It is shown that time reversibility of Hamiltonian microscopic dynamics and Gibbs canonical statistical ensemble of initial conditions for it together produce an exact virial expansion for probability distribution of path of molecular…
The thermodynamic maximum principle for the Boltzmann-Gibbs-Shannon (BGS) entropy is reconsidered by combining elements from group and measure theory. Our analysis starts by noting that the BGS entropy is a special case of relative entropy.…
The relativistic spinning particle model, proposed in [3,4], is analyzed in a Hamiltonian framework. The spin is simulated by extending the configuration space by introducing a light-like four vector degree of freedom. The model is heavily…
This paper discusses the thermodynamic irreversibility realized in high-dimensional Hamiltonian systems with a time-dependent parameter. A new quantity, the irreversible information loss, is defined from the Lyapunov analysis so as to…
Models of bounded rationality include quantum--like (QL) models, which use Hilbert--space amplitudes to represent context and order effects, and entropy--regularised (ER) models, including rational inattention, which smooth expected utility…
We study the long-term average evolution of the random ensemble along integrable Hamiltonian systems with time $T$-periodic transitions. More precisely, for any observable $G$, it is demonstrated that the ensemble under $G$ in long time…
We present a stochastic model for amplifying, diffusive media like, for instance, random lasers. Starting from a simple random-walk model, we derive a stochastic partial differential equation for the energy field with contains a…