?
New approach to classical thermodynamics
Mathematical notes. 2016. Vol. 100. No. 1. P. 154–185.
The author constructs a new conception of thermodynamics which is based on new results in number theory. We consider a maximally wide range of gases, liquids, and fluids to which, in principle, the Carathéodory approach can be applied. The Carathéodory principle is studied using the Lennard-Jones potential as an example. On the basis of this example, we analyze the dispersive structure of a fluidwhose density exceeds the critical value. We introduce a new parameter, the “jamming factor,” which determines the jamming effect for such fluids. A comparison with experimental data for nonpolar molecules is carried out. The phase transition “liquid-amorphous solid” is studied in detail in the domain of negative pressures. We discuss the theoretical relationship between the obtained solutions and econophysics, some mysteries in biology, and other sciences.
Keywords: Zeno lineBose–Einstein distributionLagrangian manifoldBachinskii conditionLennard-Jones potentialGentile correctionCarathéodory conceptioncontact manifolddispersive mediumentropy productionFermi–Dirac distributionHougen–Watson diagramLegendre manifoldphase transition “liquid-amorphous solid”van der Waals equation of statevan der Waals law of corresponding states
Pochinka O., Shmukler V., / Series math.RT "arXiv:1808.06395 [math.RT]". 2026.
Anosov flows have a long and rich history, firstly motivated by the
study of geodesic flows in negative curvature surface by Anosov and Sinai.
Not every closed manifold admits an Anosov flow for well-known reasons:
the fundamental group of a 3-manifold M admitting an Anosov flow must
have exponential growth, and M must be universally covered by R3. Nevertheless,
there ...
Added: August 31, 2026
Shabanov N., Kuricheva O., Kurbatova J. et al., / Series Working Papers SSRN "Department of Economics Ca’ Foscari University of Venice". 2026.
The carbon balance of an ecosystem is the difference between Gross Primary Productivity (GPP) and Ecosystem Respiration (Reco) as expressed by Net Ecosystem Exchange (NEE). While remote sensing retrievals of GPP have reached maturity, Reco estimation remains underexplored and ultimately cast bias on NEE. Here we present an end-to-end multi-scale analysis of the mechanism of ...
Added: August 21, 2026
Ponomarenko A., / Series Computer Science "arxiv.org". 2025.
This paper addresses the challenge of merging hierarchical navigable small world (HNSW) graphs, a critical operation for distributed systems, incremental indexing, and database compaction. We propose three algorithms for this task: Naive Graph Merge (NGM), Intra Graph Traversal Merge (IGTM), and Cross Graph Traversal Merge (CGTM). These algorithms differ in their approach to vertex selection ...
Added: July 30, 2026
Loubenets E. R., / Series arxiv.org "quant-ph". 2026. No. 2607.18050.
In many quantum applications it is important to know whether or not a Bell nonlocal two-qudit state exhibits its nonlocality under correlation scenarios with some given numbers S1,S2≥1 of generalized quantum measurements at two sites. In the present article, we find analytically a new general locality condition sufficient for a nonseparable Werner state with a ...
Added: July 21, 2026
Bolbachan V., / Series math "arxiv.org". 2024.
Chow polylogarithms are some special functions arising in explicit description of the Beilinson regulator map. The most interesting functional equation for this function reflects its vanishing on the boundary in the Bloch's cycle complex. We show that this functional equation formally follows from more simple ones, namely skew-symmetry, functoriality and multiplicativity.
To prove this, we study ...
Added: July 16, 2026
Bolbachan V., / Series math "arxiv.org". 2024.
Let K be a field of characteristic zero. We prove that its motivic cohomology in degree m−1 and weight m is rationally isomorphic to the cohomology of the polylogarithmic complex. This gives a partial extension of A. Suslin theorem describing the indecomposable K3 of a field. ...
Added: July 16, 2026
Panov V., Ryabchenko A., / Series arXiv "stat.ME". 2026. No. 2607.05048.
This paper investigates the problem of statistical inference for a mixture distribution consisting of a discrete and a continuous component, with a particular focus on the class of rational-infinitely divisible distributions. We consider non-parametric estimation of both components of the mixture as well as the quasi-L{é}vy measure, assuming that the mixture belongs to the class ...
Added: July 9, 2026
Piontkovski D., / Series arXiv "math". 2026.
A noncommutative projective variety is defined, following Artin and Zhang, by a graded coherent algebra 𝐴. The category of coherent sheaves is then the quotient qgr(𝐴) of the category of finitely presented graded modules by the subcategory of torsion modules. We consider the categorical and polynomial entropies of the Serre twist, that is, of the ...
Added: June 23, 2026
Piontkovski D., / Series arXiv "math". 2025.
If a symmetric multilinear algebra is weakly nil, then it is Engel. This result may be regarded as an infinite-dimensional analogue of the well-known Jacobian theorem, which states that if a polynomial mapping has a polynomial inverse, then its Jacobian matrix is invertible. This refines a theorem of Gerstenhaber and partially answers a question posed ...
Added: June 23, 2026
Konakov V., Kucher D., Mammen E., / Series arXiv "math". 2026. No. 2606.11142v1.
In this paper, we construct strong approximations for discrete-time Markov chains weakly converging to continuous diffusion processes, as well as for their perturbed counterparts. Under the assumption of bounded coefficients, we construct closely coupled versions of these processes on a shared probability space. In particular, for both non-degenerate and degenerate cases, we maximize the probability ...
Added: June 11, 2026
Shipilov F., Barnyakov A., Ivanov A. et al., / Series Physics "arxiv.org". 2026.
A fast simulation of the detector response is a vital task in high-energy physics (HEP). Traditional Monte-Carlo methods form the backbone of modern particle physics simulation software but are computationally expensive. We present a machine-learning-based approach to fast simulation of the Focusing Aerogel Ring Imaging Cherenkov (FARICH) detector response. Given a particle track and momentum, ...
Added: May 19, 2026
Dorovskiy A., / Series arXiv "math". 2026.
In this paper the structural stability of generic families of vector fields of the PC-HC class on the two-dimensional sphere is proved. A classification of these families up to moderate equivalence in neighborhoods of their large bifurcation supports is presented, based on such invariants as the configuration and the characteristic set. The realization lemma is proved. ...
Added: May 14, 2026
Taletskii D., / Series arXiv "math". 2026.
A vertex subset of a graph is called a \textit{distance-$k$ independent set} if the distance between any two of its distinct vertices is at least $k + 1$. For all $n,k \geq 1$, we determine the minimum possible number of inclusion-wise maximal distance-$k$ independent sets among all $n$-vertex trees. It equals~$n$ if $n \leq k ...
Added: May 1, 2026
Ovcharenko M., / Series arXiv "math". 2026.
We introduce an explicit class of tempered Laurent polynomials in the sense of Villegas and Doran--Kerr in n⩽4 variables including all Landau--Ginzburg models for smooth Fano threefolds with very ample anticanonical class. We check that it contains Landau--Ginzburg models for various Fano fourfolds which are complete intersections in smooth toric varieties and Grassmannians of planes, ...
Added: April 30, 2026
Puzachenko Y. G., Sandlerskiy R., Sankovski A. G., Ecological Modelling 2016 Vol. 341 P. 27–36
The paper addresses the spatio-temporal dynamics of biosphere reflected by the multispectral MODIS images. The hypotheses of different goal functions are examined and principles of biosphere function are tested. It is demonstrated that one of the major bishopric “goal functions” is the maintenance of the stable solar radiation absorption in the PAR range during the ...
Added: March 27, 2022
Kuricheva O., Mamkin V., Sandlerskiy R. et al., Entropy 2017 Vol. 19 No. 43 P. 1–16
Entropy production (σ) is a measure of ecosystem and landscape stability in a changing environment. We calculated the σ in the radiation balance for a well-drained spruce forest, a paludified spruce forest, and a bog in the southern taiga of the European part of Russia using long-term meteorological data. Though radiative σ depends both on surface temperature and absorbed ...
Added: March 27, 2022
Kolokoltsov V., Transactions of the Moscow Mathematical Society 2021 Vol. 82 No. 1 P. 93–104
Combining intuitive probabilistic assumptions with the basic laws of classical thermodynamics, using
the latter to express probabilistic parameters in terms of the thermodynamic quantities, we get a simple
unified derivation of the fundamental ensembles of statistical physics avoiding any limiting procedures,
quantum hypothesis and even statistical entropy maximization. This point of view leads also to some
related classes of ...
Added: October 29, 2021
Nikolskiy V., Stegailov V., , in: Параллельные Вычислительные Технологии (ПАВТ'2018) Ростов-на-Дону, 02-06 апреля 2018 г.: Челябинск: Издательский центр ЮУрГУ, 2018. P. 139–152.
One of the most important problems for the creation of exaflops supercomputer is the reduction in the energy consumption of hardware. In this paper, the many-core processor architecture Epiphany is considered as a promising energy-efficient technology. The review of programming methods for new hardware is conducted, the development and debugging of the algorithm of classical ...
Added: October 30, 2019
Maslov V. P., Russian Journal of Mathematical Physics 2018 Vol. 25 No. 2 P. 220–232
It is proved that the distributions of the analytic number theory coincide with
the Bose–Einstein distribution. The transition of the boson branch of the decomposition of
an integer number (with repeated terms) into the fermion branch (without repeated terms) is
described in detail near a small activity. Analytic formulas for the energy of transition of the
Bose gas to ...
Added: December 9, 2018
Maslov V. P., Mathematical notes 2018 Vol. 103 No. 4 P. 616–620
A relation between the jump of spin and the corresponding jump of energy is derived. This relation is used to determine the binding energy of the nucleus and the “entanglement” energy between two bosons. The latter is shown to be inversely proportional to the area in the two-dimensional case. ...
Added: December 8, 2018
Maslov V. P., Mathematical notes 2017 Vol. 102 No. 4 P. 583–586
Added: November 17, 2018
Maslov V., Теоретическая и математическая физика 2018 Т. 196 № 1 С. 161–166
Since the deep paper by Bohr and Kalckar in 1938, it has been known that the Ramanujan formula in
number theory is related to statistical physics and nuclear theory. From the early 1970s, there have been
attempts to generalize number theory from the space of integers to the space of rational numbers, i.e., to
construct a so-called analytic ...
Added: October 30, 2018
Maslov V. P., Mathematical notes 2017 Vol. 101 No. 3 P. 488–496
Abstract—Regularization of the Bose–Einstein distribution using a parastatistical correction,
i.e., by means of the Gentile statistics, is carried out. It is shown that the regularization result
asymptotically coincides with the Erdo˝ s formula obtained by using Ramanujan’s formula for the
number of variants of the partition of an integer into summands. TheHartley entropy regarded as the
logarithm of the ...
Added: October 28, 2018
Maslov V., Mathematical notes 2017 Vol. 101 No. 4 P. 660–665
In the paper “The relationship between the Fermi–Dirac distribution and statistical
distributions in languages” (This issue of “Math. Notes”), the Bose–Einstein and Fermi–Dirac
distributions are considered in connectionwith frequency distributions in languages in the context of
the author’s approach to thermodynamics and number theory problems. The present article presents
certain clarifications of certain notions used in that approach, in ...
Added: October 28, 2018