Related papers: Generalized Uncertainty Relation Between an Observ…
We analyze general uncertainty relations and we show that there can exist such pairs of non--commuting observables $A$ and $B$ and such vectors that the lower bound for the product of standard deviations $\Delta A$ and $\Delta B$ calculated…
Fluctuation theorems are fundamental results in non-equilibrium thermodynamics. Considering the fluctuation theorem with respect to the entropy production and an observable, we derive a new thermodynamic uncertainty relation which also…
We show within a statistical model of quantization reported in the previous work based on Hamilton-Jacobi theory with a random constraint that the statistics of fluctuations of the actual trajectories around the classical trajectories in…
This paper aims at investigating the influence of space-time curvature on the uncertainty relation. In particular, relying on previous findings, we assume the quantum wave function to be confined to a geodesic ball on a given space-like…
We present a simple scheme to evaluate linear response functions including quantum fluctuation corrections on top of the Gutzwiller approximation. The method is derived for a generic multi-band lattice Hamiltonian without any assumption…
Uncertainty principle is the basis of quantum mechanics. It reflects the basic law of the movement of microscopic particles. Wigner-Yanase skew information, as a measure of quantum uncertainties, is used to characterize the intrinsic…
Generalized uncertainty principles are effective changes to the Heisenberg uncertainty principle that emerge in several quantum gravity models. In the present letter, we study the consequences that two classes of these modifications yield…
For classical field theories with probabilistic initial conditions the classical field observables are an idealization. Their arbitrarily precise values poorly reflect the characteristic uncertainty in the presence of substantial…
Textbook quantum mechanics treats time as a classical parameter, and not as a quantum observable with an associated Hermitian operator. For this reason, to make sense of usual time-energy uncertainty relations such as $\Delta {t}\Delta…
Quantum measurements are inherently probabilistic and quantum theory often forbids to precisely predict the outcomes of simultaneous measurements. This phenomenon is captured and quantified through uncertainty relations. Although studied…
We derive a quantum extension of the thermodynamic uncertainty relation where dynamical fluctuations are quantified by the Terletsky-Margenau-Hill quasiprobability, a quantum generalization of the classical joint probability. The obtained…
In this work, I derive the time-dependent probability density function of classical observables using the Hamiltonian mechanics approach, extending the notion of fluctuation theorems for any observables. In particular, the time-dependent…
For a pair of observables, they are called "incompatible", if and only if the commutator between them does not vanish, which represents one of the key features in quantum mechanics. The question is, how can we characterize the…
We formulate uncertainty relations for arbitrary finite number of incompatible observables. Based on the sum of variances of the observables, both Heisenberg-type and Schr\"{o}dinger-type uncertainty relations are provided. These new lower…
The classical and quantum evolution of a generic probability distribution is analyzed. To that end, a formalism based on the decomposition of the distribution in terms of its statistical moments is used, which makes explicit the differences…
The quantization of time-reparametrization invariant systems such as general relativity is plagued by an ambiguity relating to the role of time in the theory. If one parametrizes observables by the (unobservable) time, and then relies on…
In this paper I propose a branch point twist field approach to computing a temporal entropy, that is, an entanglement measure across different time regions, as opposed to the usual spacial measures. I discuss how the shift to…
We present a general framework and procedure to derive uncertainty relations for observables of quantum systems in a covariant manner. All such relations are consequences of the positive semidefiniteness of the density matrix of a general…
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…
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…