Magic Numbers and Mixing Degree in Many-Fermion Systems

We consider an N fermion system at low temperature T in which we encounter special particle number values (Formula presented.) exhibiting special traits. These values arise when focusing attention upon the degree of mixture (DM) of the pertinent quantum states. Given the coupling constant of the Hamiltonian, the DMs stay constant for all N-values but experience sudden jumps at the (Formula presented.). For a quantum state described by the matrix (Formula presented.), its purity is expressed by (Formula presented.) and then the degree of mixture is given by (Formula presented.), a quantity that coincides with the entropy (Formula presented.) for (Formula presented.). Thus, Tsallis entropy of index two faithfully represents the degree of mixing of a state, that is, it measures the extent to which the state departs from maximal purity. Macroscopic manifestations of the degree of mixing can be observed through various physical quantities. Our present study is closely related to properties of many-fermion systems that are usually manipulated at zero temperature. Here, we wish to study the subject at finite temperature. The Gibbs ensemble is appealed to. Some interesting insights are thereby gained.Fil: Monteoliva, D.. Universidad Nacional de La Plata; Argentina. Provincia de Buenos Aires. Gobernación. Comisión de Investigaciones Científicas; ArgentinaFil: Plastino, Ángel Luis. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - La Plata. Instituto de Física La Plata. Universidad Nacional de La Plata. Facultad de Ciencias Exactas. Instituto de Física La Plata; ArgentinaFil: Plastino, Ángel Ricardo. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Universidad Nacional del Noroeste de la Provincia de Buenos Aires. Centro de Bioinvestigaciones (Sede Junín); Argentin

Reciprocity relations for quantum systems based on Fisher information

We study reciprocity relations between fluctuations of the probability distributions corresponding to position and momentum, and other observables, in quantum theory. These kinds of relations have been previously studied in terms of quantifiers based on the Lipschitz constants of the concomitant distributions. However, it turned out that they were not valid for all states. Here, we ask the following question: can those relations be described using other quantifiers? By appealing to the Fisher information, we study reciprocity relations for different families of states. In particular, we look for a connection of this problem with previous works.Instituto de Física La Plat

Magic Numbers and Mixing Degree in Many-Fermion Systems

We consider an N fermion system at low temperature T in which we encounter special particle number values Nₘ exhibiting special traits. These values arise when focusing attention upon the degree of mixture (DM) of the pertinent quantum states. Given the coupling constant of the Hamiltonian, the DMs stay constant for all N-values but experience sudden jumps at the Nm. For a quantum state described by the matrix ρ, its purity is expressed by Trρ² and then the degree of mixture is given by 1 − Trρ², a quantity that coincides with the entropy Sq for q = 2. Thus, Tsallis entropy of index two faithfully represents the degree of mixing of a state, that is, it measures the extent to which the state departs from maximal purity. Macroscopic manifestations of the degree of mixing can be observed through various physical quantities. Our present study is closely related to properties of many-fermion systems that are usually manipulated at zero temperature. Here, we wish to study the subject at finite temperature. The Gibbs ensemble is appealed to. Some interesting insights are thereby gained.Instituto de Física La Plat

An automatic entropy method to efficiently mask histology whole-slide images

Tissue segmentation of histology whole-slide images (WSI) remains a critical task in automated digital pathology workflows for both accurate disease diagnosis and deep phenotyping for research purposes. This is especially challenging when the tissue structure of biospecimens is relatively porous and heterogeneous, such as for atherosclerotic plaques. In this study, we developed a unique approach called 'EntropyMasker' based on image entropy to tackle the fore- and background segmentation (masking) task in histology WSI. We evaluated our method on 97 high-resolution WSI of human carotid atherosclerotic plaques in the Athero-Express Biobank Study, constituting hematoxylin and eosin and 8 other staining types. Using multiple benchmarking metrics, we compared our method with four widely used segmentation methods: Otsu's method, Adaptive mean, Adaptive Gaussian and slideMask and observed that our method had the highest sensitivity and Jaccard similarity index. We envision EntropyMasker to fill an important gap in WSI preprocessing, machine learning image analysis pipelines, and enable disease phenotyping beyond the field of atherosclerosis

Beyond Boltzmann–Gibbs–Shannon in Physics and Elsewhere

The pillars of contemporary theoretical physics are classical mechanics, Maxwell electromagnetism, relativity, quantum mechanics, and Boltzmann–Gibbs (BG) statistical mechanics –including its connection with thermodynamics. The BG theory describes amazingly well the thermal equilibrium of a plethora of so-called simple systems. However, BG statistical mechanics and its basic additive entropy S B G started, in recent decades, to exhibit failures or inadequacies in an increasing number of complex systems. The emergence of such intriguing features became apparent in quantum systems as well, such as black holes and other area-law-like scenarios for the von Neumann entropy. In a different arena, the efficiency of the Shannon entropy—as the BG functional is currently called in engineering and communication theory—started to be perceived as not necessarily optimal in the processing of images (e.g., medical ones) and time series (e.g., economic ones). Such is the case in the presence of generic long-range space correlations, long memory, sub-exponential sensitivity to the initial conditions (hence vanishing largest Lyapunov exponents), and similar features. Finally, we witnessed, during the last two decades, an explosion of asymptotically scale-free complex networks. This wide range of important systems eventually gave support, since 1988, to the generalization of the BG theory. Nonadditive entropies generalizing the BG one and their consequences have been introduced and intensively studied worldwide. The present review focuses on these concepts and their predictions, verifications, and applications in physics and elsewhere. Some selected examples (in quantum information, high- and low-energy physics, low-dimensional nonlinear dynamical systems, earthquakes, turbulence, long-range interacting systems, and scale-free networks) illustrate successful applications. The grounding thermodynamical framework is briefly described as well