Abstract:
Mathematical models with mean field and local type interaction are considered in connection with stochastic chemical kinetics. Special emphasis is placed on various notions of reversibility, their consequences (Boltzmann type equations, fluctuations, Onsager relations, and so on), and the emergence of irreversibility.
This publication is cited in the following 28 articles:
Evgenia Gasnikova, Alexander Gasnikov, Yaroslav Kholodov, Anastasiya Zukhba, “An Evolutionary View on Equilibrium Models of Transport Flows”, Mathematics, 11:4 (2023), 858
V. V. Vedenyapin, S. Z. Adzhiev, V. V. Kazantseva, “Boltzmann and Poincaré Entropy, Boltzmann Extremals, and Hamilton–Jacobi Method for Non-Hamiltonian Situation”, J Math Sci, 260:4 (2022), 434
S. Z. Adzhiev, V. V. Vedenyapin, I. V. Melikhov, “Kinetic aggregation models leading to morphological memory of formed structures”, Comput. Math. Math. Phys., 62:2 (2022), 254–268
Ya. G. Batishcheva, “Cauchy problem for a new aggregation–fragmentation model in the case of equal reaction rate constants”, Comput. Math. Math. Phys., 62:3 (2022), 452–466
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D. R. Baymurzina, A. V. Gasnikov, E. V. Gasnikova, P. E. Dvurechenskii, E. I. Ershov, M. B. Kubentayeva, A. A. Lagunovskaya, “Universal method of searching for equilibria and stochastic equilibria in transportation networks”, Comput. Math. Math. Phys., 59:1 (2019), 19–33
Sergey Adzhiev, Janina Batishcheva, Igor Melikhov, Victor Vedenyapin, “Kinetic Equations for Particle Clusters Differing in Shape and the H-theorem”, Physics, 1:2 (2019), 229
A. Gasnikov, P. Dvurechensky, M. Zhukovskii, S. Kim, S. Plaunov, D. Smirnov, F. Noskov, “About the power law of the PageRank vector distribution. Part 2. Backley–Osthus model, power law verification for this model and setup of real search engines”, Num. Anal. Appl., 11:1 (2018), 16–32
V. V. Vedenyapin, S. Z. Adzhiev, V. V. Kazantseva, “Entropiya po Boltsmanu i Puankare, ekstremali Boltsmana i metod Gamiltona–Yakobi v negamiltonovoi situatsii”, Differentsialnye i funktsionalno-differentsialnye uravneniya, SMFN, 64, no. 1, Rossiiskii universitet druzhby narodov, M., 2018, 37–59
A. Gasnikov, E. Gasnikova, P. Dvurechensky, A. Mohammed, E. Chernousova, “About the power law of the PageRank vector distribution. Part 1. Numerical methods for finding the PageRank vector”, Num. Anal. Appl., 10:4 (2017), 299–312
Adzhiev S.Z. Melikhov I.V. Vedenyapin V.V., “The H-Theorem For the Physico-Chemical Kinetic Equations With Explicit Time Discretization”, Physica A, 481 (2017), 60–69
S. Z. Adzhiev, I. V. Melikhov, V. V. Vedenyapin, “The H-theorem for the physico-chemical kinetic equations with discrete time and for their generalizations”, Phys. A, 480 (2017), 39–50
S. Adzhiev, I. Melikhov, V. Vedenyapin, “The H-Theorem For the Chemical Kinetic Equations With Discrete Time and For Their Generalizations”, V International Conference on Problems of Mathematical and Theoretical Physics and Mathematical Modelling, Journal of Physics Conference Series, 788, IOP Publishing Ltd, 2017, UNSP 012001
S. Z. Adzhiev, V. V. Vedenyapin, Yu. A. Volkov, I. V. Melikhov, “Generalized Boltzmann-type equations for aggregation in gases”, Comput. Math. Math. Phys., 57:12 (2017), 2017–2029
A. V. Gasnikov, E. V. Gasnikova, Yu. E. Nesterov, A. V. Chernov, “Efficient numerical methods for entropy-linear programming problems”, Comput. Math. Math. Phys., 56:4 (2016), 514–524
A. V. Gasnikov, E. V. Gasnikova, M. A. Mendel, K. V. Chepurchenko, “Evolyutsionnye vyvody entropiinoi modeli rascheta matritsy korrespondentsii”, Matem. modelirovanie, 28:4 (2016), 111–124
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Alvise Bastianello, Spyros Sotiriadis, “Cluster expansion for ground states of local Hamiltonians”, Nuclear Physics B, 909 (2016), 1020