On Relativistic Generalization of Perelman's W-entropy and Statistical Thermodynamic Description of Gravitational Fields

Using double 2+2 and 3+1 nonholonomic fibrations on Lorentz manifolds, we extend the concept of W-entropy for gravitational fields in the general relativity, GR, theory. Such F- and W-functionals were introduced in the Ricci flow theory of three dimensional, 3-d, Riemannian metrics by G. Perelman, arXiv: math.DG/0211159. Nonrelativistic 3-d Ricci flows are characterized by associated statistical thermodynamical values determined by W--entropy. Generalizations for geometric flows of 4-d pseudo-Riemannian metrics are considered for models with local thermodynamical equilibrium and separation of dissipative and non-dissipative processes in relativistic hydrodynamics. The approach is elaborated in the framework of classical filed theories (relativistic continuum and hydrodynamic models) without an underlying kinetic description which will be elaborated in other works. The 3+1 splitting allows us to provide a general relativistic definition of gravitational entropy in the Lyapunov-Perelman sense. It increases monotonically as structure forms in the Universe. We can formulate a thermodynamic description of exact solutions in GR depending, in general, on all spacetime coordinates. A corresponding 2+2 splitting with nonholonomic deformation of linear connection and frame structures is necessary for generating in very general form various classes of exact solutions of the Einstein and general relativistic geometric flow equations. Finally, we speculate on physical macrostates and microstate interpretations of the W-entropy in GR, geometric flow theories and possible connections to string theory (a second unsolved problem also contained in Perelman's works) in the Polyakov's approach.Comment: latex2e, v4 is an accepted to EPJC substantial extension of a former letter type paper on 10 pages to a research article on 41 pages; a new author added, the paper's title and permanent and visiting affiliations were correspondingly modified; and new results, conclusions and references are provide

Fish occurrence in the middle Volga and upper Don regions (Russia)

In ichthyological publications from both Russia as a whole, and from the study region, lack of data indicating the actual results of observations in a specific place all result in publication of a generalised analysis. Although our publications contain such data, they are, however, not convenient for users performing global analysis. The main purpose of publishing a database is to make our data available in the global biodiversity system to a wide range of users. Dataset represents a significant addition to the distribution of species in this area. The data can be used to analyse future changes in ichthyofauna, as well as to help the authorities to manage their territory more efficiently.This publication describes a dataset that contains information on fish encounters in the Upper Don basin and the middle Volga (centre of the European part of Russia) over a 30-year period (1990-2020). The dataset contains information on 6400 occurrences of 394341 specimens of 56 species, 99.9% of specimens being identified to the species level. A total of 883 sites were studied, of which 253 were in lentic biotopes (lakes - 121, ponds - 123, backwater - 5, reservoir - 3, pit - 1), 630 were in lotic (rivers - 628, stream - 1, channel - 1). One collecting site has an average of 7.2 species (from 1-21 species per location). Only those species that form self-reproducing populations are given. The dataset is a compilation of data from several working author groups. All observations have precise geo-referencing with the names of water bodies (rivers, lakes etc.). All presented data are published in the form of a database for the first time. Some data form the basis of previously-published works (3998 observations, 62%) and some are published for the first time (2402 observations, 38%). A large amount of data comes from small water bodies that have been neglected by previous researchers