Related papers: Atomic Entailment and Atomic Inconsistency and Cla…

In spite of its popularity, it has not been possible to vindicate the conventional wisdom that classical mechanics is a limiting case of quantum mechanics. The purpose of the present paper is to offer an alternative formulation of classical…

The definition of "classical anomaly" is introduced. It describes the situation in which a purely classical dynamical system which presents both a lagrangian and a hamiltonian formulation admits symmetries of the action for which the…

Let A be a finite or countable alphabet and let $\theta$ be a literal (anti-)automorphism onto A * (by definition, such a correspondence is determinated by a permutation of the alphabet). This paper deals with sets which are invariant under…

Trustworthy AI requires reasoning systems that are not only powerful but also transparent and reliable. Automated Theorem Proving (ATP) is central to formal reasoning, yet classical binary resolution remains limited, as each step involves…

We consider one-dimensional classical time-dependent Hamiltonian systems with quasi-periodic orbits. It is well-known that such systems possess an adiabatic invariant which coincides with the action variable of the Hamiltonian formalism. We…

We propose new algebraic invariants that distinguish and classify entangled states. Considering qubits as well as higher spin systems, we obtained complete entanglement classifications for cases that were either unsolved or only conjectured…

Quantum uncertainty is the cornerstone of quantum mechanics which underlies many counterintuitive nonclassical phenomena. Recent studies remarkably showed that it also fundamentally limits nonclassical correlation, and crucially, a…

The investigation of quantum-classical correspondence may lead to gain a deeper understanding of the classical limit of quantum theory. We develop a quantum formalism on the basis of a linear-invariant theorem, which gives an exact…

We are lifting classical problems from single instances to regular sets of instances. The task of finding a positive instance of the combinatorial problem $P$ in a potentially infinite given regular set is equivalent to the so called…

The concept of structural invariance previously introduced by the authors is used to argue that the connection between random matrix theory and quantum systems with a chaotic classical counterpart is in fact largely exact in the…

As it is well known, classical mechanics consists of several basic features like determinism, reductionism, completeness of knowledge and mechanicism. In this article the basic assumptions are discussed which underlie those features. It is…

Modern quantum chemistry can make quantitative predictions on an immense array of chemical systems. However, the interpretation of those predictions is often complicated by the complex wave function expansions used. Here we show that an…

A direct classical analog of quantum decoherence is introduced. Similarities and differences between decoherence dynamics examined quantum mechanically and classically are exposed via a second-order perturbative treatment and via a strong…

The Quantum Decision Theory, developed recently by the authors, is applied to clarify the role of risk and uncertainty in decision making and in particular in relation to the phenomenon of dynamic inconsistency. By formulating this notion…

There is a problem with the foundations of classical mathematics, and potentially even with the foundations of computer science, that mathematicians have by-and-large ignored. This essay is a call for practicing mathematicians who have been…

Defining the entropy of classical particles raises a number of paradoxes and ambiguities, some of which have been known for over a century. Several, such as Gibbs' paradox, involve the fact that classical particles are distinguishable, and…

Building on our previous work on enriched universal algebra, we define a notion of enriched language consisting of function and relation symbols whose arities are objects of the base of enrichment. In this context, we construct atomic…

The expansion of a classical Hamilton formalism consisting in adaptation of it to describe the nonequilibrium systems is offered. Expansion is obtained by construction of formalism on the basis of the dynamics equation of the equilibrium…

One of the best signatures of nonclassicality in a quantum system is the existence of correlations that have no classical counterpart. Different methods for quantifying the quantum and classical parts of correlations are amongst the more…

I argue that scientific determinism is not supported by facts, but results from the elegance of the mathematical language physicists use, in particular from the so-called real numbers and their infinite series of digits. Classical physics…