Related papers: Random Dynamics, Entropy Production and Fisher Inf…
The principle of maximum entropy (Maxent) is often used to obtain prior probability distributions as a method to obtain a Gibbs measure under some restriction giving the probability that a system will be in a certain state compared to the…
We consider the task of filtering a dynamic parameter evolving as a diffusion process, given data collected at discrete times from a likelihood which is conjugate to the marginal law of the diffusion, when a generic dual process on a…
It is a great challenge of nonequilibrium statistical mechanics to calculate entropy production within a microscopic theory. In the framework of linear irreversible thermodynamics, we combine the Mori-Zwanzig-Forster projection operator…
These lectures deal with the problem of inductive inference, that is, the problem of reasoning under conditions of incomplete information. Is there a general method for handling uncertainty? Or, at least, are there rules that could in…
Uncertainty propagation and filtering can be interpreted as gradient flows with respect to suitable metrics in the infinite dimensional manifold of probability density functions. Such a viewpoint has been put forth in recent literature, and…
The principle of maximum entropy is a broadly applicable technique for computing a distribution with the least amount of information possible while constrained to match empirically estimated feature expectations. However, in many real-world…
Hidden information emerges under impulse interactions with Markov diffusion process modeling interactive random environment. Impulse yes no action cuts Markov correlations revealing Bit of hidden information connected correlated states.…
A central concept in the connection between physics and information theory is entropy, which represents the amount of information extracted from the system by the observer performing measurements in an experiment. Indeed, Jaynes' principle…
The Fisher information of a quantum observable is shown to be proportional to both (i) the difference of a quantum and a classical variance, thus providing a measure of nonclassicality; and (ii) the rate of entropy increase under Gaussian…
Macroscopic traffic flow is stochastic, but the physics-informed deep learning methods currently used in transportation literature embed deterministic PDEs and produce point-valued outputs; the stochasticity of the governing dynamics plays…
Entropy and the fluctuation-dissipation theorem are at the heart of statistical mechanics near equilibrium. Driving a system beyond the linear response regime leads to (i) the breakdown of the fluctuation-dissipation theorem and (ii) a…
By considering an explicit nonequilibrium model, we analyze the statistics of the irreversible work, $w_{\rm irr}$, and irreversible entropy production, $\Delta_i s$, within the stochastic energetics framework. Restating the second law of…
These lecture notes introduce the statistical analysis of continuous-time generative models built from Markov dynamics. We begin with the stochastic-calculus foundations of score-based diffusion models, including time reversal, score…
We investigate fluctuations in the momentum flux across a surface perpendicular to the velocity gradient in a stationary shear flow maintained by either thermostated deterministic or by stochastic boundary conditions. In the deterministic…
Diffusion models have recently achieved remarkable success in generative modeling, yet they are commonly formulated as black-box stochastic systems with limited interpretability and few structural guarantees. In this paper, we establish a…
Information dynamics is an emerging description of information processing in complex systems which describes systems in terms of intrinsic computation, identifying computational primitives of information storage and transfer. In this paper…
In this work, we study the dynamics of the logistic map based on a probabilistic characterization in terms of the invariant density. We analyze the relevant regimes of the dynamics (regular, oscillatory, onset chaotic and fully chaotic) in…
Using waves to explore our environment is a widely used paradigm, ranging from seismology to radar technology, and from bio-medical imaging to precision measurements. In all of these fields, the central aim is to gather as much information…
We derive the exact evolution equation for the probability density function of particle displacements generated by arbitrary Gaussian velocity processes, when neither Markovianity and nor stationarity are assumed. Starting from the…
Linear, irreversible thermodynamics predicts that the entropy production rate can become negative. We demonstrate this prediction for metals under AC-driving whose conductivity is well-described by the Drude-Sommerfeld model. We then show…