Топологическая унифицированная (r,s)-энтропия непрерывных отображений в квазиметрических пространствах

The category of metric spaces is a subcategory of quasi-metric spaces. It is shown that the entropy of a map when symmetric properties is included is greater or equal to the entropy in the case that the symmetric property of the space is not considered. The topological entropy and Shannon entropy have similar properties such as nonnegativity, subadditivity and conditioning reduces entropy. In other words, topological entropy is supposed as the extension of classical entropy in dynamical systems. In the recent decade, different extensions of Shannon entropy have been introduced. One of them which generalizes many classical entropies is unified $(r,s)$-entropy. In this paper, we extend the notion of unified $(r, s)$-entropy for the continuous maps of a quasi-metric space via spanning and separated sets. Moreover, we survey unified $(r, s)$-entropy of a map for two metric spaces that are associated with a given quasi-metric space and compare unified $(r, s)$-entropy of a map of a given quasi-metric space and the maps of its associated metric spaces. Finally we define Tsallis topological entropy for the continuous map on a quasi-metric space via Bowen's definition and analyze some properties such as chain rule.

Semi-device-independent random number generation with flexible assumptions

Our ability to trust that a random number is truly random is essential for fields as diverse as cryptography and fundamental tests of quantum mechanics. Existing solutions both come with drawbacks—device-independent quantum random number generators (QRNGs) are highly impractical and standard semi-device-independent QRNGs are limited to a specific physical implementation and level of trust. Here we propose a framework for semi-device-independent randomness certification, using a source of trusted vacuum in the form of a signal shutter. It employs a flexible set of assumptions and levels of trust, allowing it to be applied in a wide range of physical scenarios involving both quantum and classical entropy sources. We experimentally demonstrate our protocol with a photonic setup and generate secure random bits under three different assumptions with varying degrees of security and resulting data rates.

A Hybrid Weight Assignment Model for Urban Underground Space Resources Evaluation Integrated with the Weight of Time Dimension

The utilization of urban underground space resources (UUSR) are important approaches to effectively save land resources, improve the living environment, expand the urban space, and achieve sustainable urban development. To obtain accurate UUSR evaluation results, the weight assignment of indicators plays an important role in the evaluation process and is an indispensable part of it. Reasonable weights of indicators can greatly improve the accuracy of the final UUSR evaluation results. Neither the basic characteristics of cross-section data and time series data of UUSR evaluation indicators are taken into consideration simultaneously, nor is the combination and cross application of different weighting methods in the previous weight assignment of UUSR evaluation indicators. Considering the influence of the time dimension, the weighting method of time dimension is introduced into the UUSR evaluation. Through integrating the classical entropy weight method, which is a frequently-used weighting method of indicator dimension with the weighting method of time dimension in two different approaches by time ordered weighted averaging (TOWA) operator, the hybrid weight assignment model named entropy and time weighting model (E-TW) for UUSR evaluation is proposed. The experimental calculation results show that the UUSR evaluation results using the E-TW model are significantly better than the results using the single classical entropy weight method, which means the hybrid weight assignment model is more suitable for UUSR evaluation than the single weighting method of indicator dimension.

Entropy and Entropy Production in Multiscale Dynamics

Heat conduction is investigated on three levels: equilibrium, Fourier, and Cattaneo. The Fourier level is either the point of departure for investigating the approach to equilibrium or the final stage in the investigation of the approach from the Cattaneo level. Both investigations bring to the Fourier level an entropy and a thermodynamics. In the absence of external and internal influences preventing the approach to equilibrium the entropy that arises in the latter investigation is the production of the classical entropy that arises in the former investigation. If the approach to equilibrium is prevented, then the entropy that arises in the investigation of the approach from the Cattaneo level to the Fourier level still brings to the Fourier level the entropy and the thermodynamics even if the classical entropy and the classical thermodynamics are absent. We also note that vanishing total entropy production as a characterization of equilibrium state is insufficient.

Examples in the entropy theory of countable group actions

Kolmogorov–Sinai entropy is an invariant of measure-preserving actions of the group of integers that is central to classification theory. There are two recently developed invariants, sofic entropy and Rokhlin entropy, that generalize classical entropy to actions of countable groups. These new theories have counterintuitive properties such as factor maps that increase entropy. This survey article focusses on examples, many of which have not appeared before, that highlight the differences and similarities with classical theory.

Celebrating Soft Matter's 10th anniversary: Testing the foundations of classical entropy: colloid experiments

By performing experiments on colloids, one can establish that certain definitions of the classical entropy fit the data, while others in the literature do not.