Related papers: Irreversibility and randomness
Conditional on the extended Riemann hypothesis, we show that with high probability, the characteristic polynomial of a random symmetric $\{\pm 1\}$-matrix is irreducible. This addresses a question raised by Eberhard in recent work. The main…
Probabilistic frames are a generalization of finite frames into the Wasserstein space of probability measures with finite second moment. We introduce new probabilistic definitions of duality, analysis, and synthesis and investigate their…
Active matter systems are driven out of equilibrium by conversion of energy into directed motion locally on the level of the individual constituents. In the spirit of a minimal description, active matter is often modeled by so-called active…
The work concentrates on relations, which are general and model independent in chaotic system, between time averages of a few (typically {\it very few}) observables. Equilibrium thermodynamics provides a guide and here is attempted to argue…
This paper examines the foundational concept of random variables in probability theory and statistical inference, demonstrating that their mathematical definition requires no reference to randomization or hypothetical repeated sampling. We…
An out of the box intellectual path exploring the foundations of quantum mechanics is discussed in some detail, in order to clarify why a possibly different way to look at the relevant fundamental questions can be identified and can support…
The appealing theoretical measure of irreversibility in a stochastic process, as the ratio of the probabilities of a trajectory and its time reversal, cannot be accessed directly in experiment since the probability of a single trajectory is…
We introduce a deterministic, time-reversible version of the Ehrenfest urn model. The distribution of first-passage times from equilibrium to non-equilibrium states and vice versa is calculated. We find that average times for transition to…
In quantum mechanics, the Heisenberg uncertainty relation presents an ultimate limit to the precision by which one can predict the outcome of position and momentum measurements on a particle. Heisenberg explicitly stated this relation for…
We introduce a distributionally robust maximum likelihood estimation model with a Wasserstein ambiguity set to infer the inverse covariance matrix of a $p$-dimensional Gaussian random vector from $n$ independent samples. The proposed model…
In a prequential approach to algorithmic randomness, probabilities for the next outcome can be forecast `on the fly' without the need for fully specifying a probability measure on all possible sequences of outcomes, as is the case in the…
A common knowledge suggests that trajectories of particles in quantum mechanics always have quantum uncertainties. These quantum uncertainties set by the Heisenberg uncertainty principle limit precision of measurements of fields and forces,…
The Lorentz gas is one of the simplest, most widely used models to study the transport properties of rarified gases in matter. It describes the dynamics of a cloud of non-interacting point particles in an infinite array of fixed spherical…
A finite dimensional quantum system for which the quantum chaos conjecture applies has eigenstates, which show the same statistical properties than the column vectors of random orthogonal or unitary matrices. Here, we consider the different…
In 1927 Heisenberg discovered that the ``more precisely the position is determined, the less precisely the momentum is known in this instant, and vice versa''. Four years later G\"odel showed that a finitely specified, consistent formal…
The Born's rule introduces intrinsic randomness to the outcomes of a measurement performed on a quantum mechanical system. But, if the system is prepared in the eigenstate of an observable then the measurement outcome of that observable is…
Explaining the emergence of stochastic irreversible macroscopic dynamics from time-reversible deterministic microscopic dynamics is one of the key problems in philosophy of physics. The Mori-Zwanzig projection operator formalism, which is…
We present a model of roundoff error analysis that combines simplicity with predictive power. Though not considering all sources of roundoff within an algorithm, the model is related to a recursive roundoff error analysis and therefore…
An attempt is made to de-mystify the apparent "paradox" between microscopic time revsersibility and macroscopic time irreversibility. It is our common experience that a hot cup of coffee cools down to room temperature and it never…
Data Science and Machine learning have been growing strong for the past decade. We argue that to make the most of this exciting field we should resist the temptation of assuming that forecasting can be reduced to brute-force data analytics.…