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We address the generalized uncertainty principle in scenarios of successive measurements. Uncertainties are characterized by means of generalized entropies of both the R\'{e}nyi and Tsallis types. Here, specific features of measurements of…
Based on string theory, black hole physics, doubly special relativity and some "thought" experiments, minimal distance and/or maximum momentum are proposed. As alternatives to the generalized uncertainty principle (GUP), the modified…
Heisenberg's uncertainty principle is usually taken to express a limitation of operational possibilities imposed by quantum mechanics. Here we demonstrate that the full content of this principle also includes its positive role as a…
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 uncertainty principle restricts potential information one gains about physical properties of the measured particle. However, if the particle is prepared in entanglement with a quantum memory, the corresponding entropic uncertainty…
Heisenberg's uncertainty principle implies fundamental constraints on what properties of a quantum system can we simultaneously learn. However, it typically assumes that we probe these properties via measurements at a single point in time.…
The entropic uncertainty measures of the multidimensional hydrogenic states quantify the multiple facets of the spatial delocalization of the electronic probability density of the system. The Shannon entropy is the most adequate uncertainty…
Observing stochastic trajectories with rare transitions between states, practically undetectable on time scales accessible to experiments, makes it impossible to directly quantify the entropy production and thus infer whether and how far…
The maximum entropy production (MEP) principle is a hypothetical law of physics which dictates that complex systems, far from equilibrium, evolve into an ordered dissipative structure (DS) which generates as much entropy per second as…
Uncertainty principle has a fundamental role in quantum theory. This principle states that it is not possible to measure two incompatible observers simultaneously. The uncertainty principle is expressed logically in terms of standard…
The uncertainty principle can be expressed in entropic terms, also taking into account the role of entanglement in reducing uncertainty. The information exclusion principle bounds instead the correlations that can exist between the outcomes…
A prominent formulation of the uncertainty principle identifies the fundamental quantum feature that no particle may be prepared with certain outcomes for both position and momentum measurements. Often the statistical uncertainties are…
Uncertainty relations are central to quantum physics. While they were originally formulated in terms of variances, they have later been successfully expressed with entropies following the advent of Shannon information theory. Here, we…
Given two orthornormal bases A and B, the basic form of the entropic uncertainty principle is stated in terms of the sum of the Shannon entropies of the probabilities of measuring A and B onto a given quantum state. State independent lower…
There is a renewed interest in the uncertainty principle, reformulated from the information theoretic point of view, called the entropic uncertainty relations. They have been studied for various integrable systems as a function of their…
Various approaches to Quantum Gravity (such as String Theory and Doubly Special Relativity), as well as black hole physics predict a minimum measurable length, or a maximum observable momentum, and related modifications of the Heisenberg…
In a previous study, it was shown that the Generalized Uncertainty Principle (GUP) can be derived from non-extensive entropies, particularly those depending only on the probability, denoted as $S_\pm$ in the literature. This finding reveals…
By introducing the generalized uncertainty principle (GUP) on the quantum state density, we calculate the statistical entropy of a scalar field on the background of (2+1)-dimensional de Sitter space without artificial cutoff. The desired…
The uncertainty relation based on the Shannon entropies of the probability densities in position and momentum spaces is improved for quantum systems in arbitrary $D$-dimensional spherically symmetric potentials. To find it, we have used the…
Statistical properties of coupled dynamic-stochastic systems are studied within a combination of the maximum information principle and the superstatistical approach. The conditions at which the Shannon entropy functional leads to a…