Related papers: Algebraic probability, classical stochastic proces…

We study the role of context, complex of physical conditions, in quantum as well as classical experiments. It is shown that by taking into account contextual dependence of experimental probabilities we can derive the quantum rule for the…

The fragmentation of diatomic molecules under a stochastic force is investigated both classically and quantum mechanically, focussing on their dissociation probabilities. It is found that the quantum system is more robust than the classical…

The idea of writing a table of probabilistic data for a quantum or classical system, and of decomposing this table in a compact way, leads to a shortcut for Hardy's formalism, and gives new perspectives on foundational issues.

We present a method for incorporating a stochastic point of view into physics exercises of mathematics education. The core of our method is the randomization of some inputs, the system model used does not differ from what we would use in…

In a previous article [H. Bergeron, J. Math. Phys. 42, 3983 (2001)], we presented a method to obtain a continuous transition from classical to quantum mechanics starting from the usual phase space formulation of classical mechanics. This…

In this paper, a connection between bi-free probability and the theory of non-commutative stochastic processes is examined. Specifically it is demonstrated that the transition operators for non-commutative stochastic processes can be…

We present the formalism of sequential and asynchronous processes defined in terms of random or quantum grammars and argue that these processes have relevance in genomics. To make the article accessible to the non-mathematicians, we keep…

An extension of the Doi-Peliti formalism for stochastic chemical kinetics is proposed. Using the extension, path-integral expressions consistent with previous studies are obtained. In addition, the extended formalism is naturally connected…

Using a group theoretical approach we derive an equation of motion for a mixed quantum-classical system. The quantum-classical bracket entering the equation preserves the Lie algebra structure of quantum and classical mechanics: The bracket…

This paper presents a categorical account of conditional probability, covering both the classical and the quantum case. Classical conditional probabilities are expressed as a certain "triangle-fill-in" condition, connecting marginal and…

Quantum mechanics contains some strange unphysical concepts. Among these are complex numbers, Hilbert spaces with their unitary and self-adjoint operators, states represented by complex vectors, superpositions of states, collapse of wave…

We deliver a call to arms for probabilistic numerical methods: algorithms for numerical tasks, including linear algebra, integration, optimization and solving differential equations, that return uncertainties in their calculations. Such…

We provide a perturbative framework to calculate extreme events of non-Markovian processes, by mapping the stochastic process to a two-species reaction diffusion process in a Doi-Peliti field theory combined with the Martin-Siggia-Rose…

In the Bayesian approach to probability theory, probability quantifies a degree of belief for a single trial, without any a priori connection to limiting frequencies. In this paper we show that, despite being prescribed by a fundamental…

In recent years, the non-relativistic quantum dynamics derived from three assumptions; i) probability current conservation, ii) average energy conservation, and iii) an epistemic momentum uncertainty [A. Budiyono and D. Rohrlich,…

We give a review of the tomographic probability representation of quantum mechanics. We present the formalism of quantum states and quantum observables using the formalism of standard probability distributions and classical-like random…

We study transformations of conventional (`classical') probabilities induced by context transitions. It is demonstrated that the transition from one complex of conditions to another induces a perturbation of the classical rule for the…

This paper argues that every quantum system can be understood as a sufficiently general kind of stochastic process unfolding in an old-fashioned configuration space according to ordinary notions of probability. This argument is based on an…

A scheme for constructing quantum mechanics is given that does not have Hilbert space and linear operators as its basic elements. Instead, a version of algebraic approach is considered. Elements of a noncommutative algebra (observables) and…

In this paper, we discuss questions related to the renormalizability of the classical statistical approximation, an approximation scheme that has been used recently in several studies of out-of-equilibrium problems in Quantum Field Theory.…