相关论文: Relation of uncertainty for time
Current statistics can be calculated in various ways. Event-based approaches use the statistics of the number of events occuring during a given time. Time-based approaches use the statistics of the time needed to reach a given number of…
Uncertainty relations play a crucial role in quantum mechanics. Well-defined methods exist for the derivation of such uncertainties for pairs of observables. Other approaches also allow the formulation of time-energy uncertainty relations,…
A central problem in uncertainty quantification is how to characterize the impact that our incomplete knowledge about models has on the predictions we make from them. This question naturally lends itself to a probabilistic formulation, by…
The problem of time is a deep paradox in our physical description of the world. According to Aristotle's relational theory, time is a measure of change and does not exist on its own. In contrast, quantum mechanics, just like Newtonian…
It is often claimed that the fundamental laws of physics are deterministic and time-symmetric and that therefore our experience of the passage of time is an illusion. This paper will critically discuss these claims and show that they are…
Although time measurements are routinely performed in laboratories, their theoretical description is still an open problem. Correspondingly, the status of the energy-time uncertainty relation is unsettled. In the first part of this work the…
A non stationary state in the one-dimensional infinite square well formed by a combination of the ground state and the first excited one is considered. The statistical complexity and the Fisher-Shannon entropy in position and momentum are…
The concept of time emerges as an ordering structure in a classical statistical ensemble. Probability distributions $p_\tau(t)$ at a given time $t$ obtain by integrating out the past and future. We discuss all-time probability distributions…
The chaotic hypothesis has several implications which have generated interest in the literature because of their generality and because a few exact predictions are among them. However its application to Physics problems requires attention…
A manifestly covariant relativistic statistical mechanics of the system of $N$ indistinguishable events with motion in space-time parametrized by an invariant ``historical time'' $\tau $ is considered. The relativistic mass distribution for…
Measurement outcomes of a quantum state can be genuinely random (unpredictable) according to the basic laws of quantum mechanics. The Heisenberg-Robertson uncertainty relation puts constrains on the accuracy of two noncommuting observables.…
We introduce a framework to identify Fluctuation Relations for vector-valued observables in physical systems evolving through a stochastic dynamics. These relations arise from the particular structure of a suitable entropic functional and…
Stochastic thermodynamics is formulated under the assumption of perfect knowledge of all thermodynamic parameters. However, in any real-world experiment, there is non-zero uncertainty about the precise value of temperatures, chemical…
Stochastic monotonicity is a well known partial order relation between probability measures defined on the same partially ordered set. Strassen Theorem establishes equivalence between stochastic monotonicity and the existence of a coupling…
A time-reversal symmetry relation is established for out-of-equilibrium dilute or rarefied gases described by the fluctuating Boltzmann equation. The relation is obtained from the associated coarse-grained master equation ruling the random…
Distinguishability plays a major role in quantum and statistical physics. When particles are identical their wave function must be either symmetric or antisymmetric under permutations and the number of microscopic states, which determines…
In this paper, we investigate the well-posedness and asymptotic behavior of difference equations of the form $x(t) = A x(t - \tau(t))$, $t \geq 0$, where the unknown function $x$ takes values in $\mathbb R^d$ for some positive integer $d$,…
Shannon information entropy is a natural measure of probability (de)localization and thus (un)predictability in various procedures of data analysis for model systems. We pay particular attention to links between the Shannon entropy and the…
Uncertainty relations are usually formulated as trade-off relations between two or more observables. Here we show that the uncertainty of a single observable already has a nontrivial lower bound originating from the noncommutativity between…
Several theoretical results concerning event-by-event fluctuations are discussed: (1) a role of the global conservation laws and concept of statistical ensembles; (2) strongly intensive measures are introduced; they give a possibility to…