157 citations · 2.9k across the 96 of their papers we have counts for
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Beyond Navier--Stokes equations: Capillarity of ideal gas
A. N. Gorban, I. V. Karlin
The system of Navier--Stokes--Fourier equations is one of the most celebrated systems of equations in modern science. It describes dynamics of fluids in the limit when gradients of…
Detailed balance in micro- and macrokinetics and micro-distinguishability of macro-processes
A. N. Gorban
We develop a general framework for the discussion of detailed balance and analyse its microscopic background. We find that there should be two additions to the well-known - or $…
General H-theorem and entropies that violate the second law
Alexander N. Gorban
-theorem states that the entropy production is nonnegative and, therefore, the entropy of a closed system should monotonically change in time. In information processing, the ent…
Thermodynamics in the Limit of Irreversible Reactions
A. N. Gorban, E. M. Mirkes, G. S. Yablonsky
For many real physico-chemical complex systems detailed mechanism includes both reversible and irreversible reactions. Such systems are typical in homogeneous combustion and hetero…
Thermodynamic Tree: The Space of Admissible Paths
A. N. Gorban
Is a spontaneous transition from a state x to a state y allowed by thermodynamics? Such a question arises often in chemical thermodynamics and kinetics. We ask the more formal ques…
Extended Detailed Balance for Systems with Irreversible Reactions
A. N. Gorban, G. S. Yablonsky
The principle of detailed balance states that in equilibrium each elementary process is equilibrated by its reverse process. For many real physico-chemical complex systems (e.g. ho…
Reciprocal Relations Between Kinetic Curves
G. S. Yablonsky, A. N. Gorban, D. Constales +2
We study coupled irreversible processes. For linear or linearized kinetics with microreversibility, , the kinetic operator is symmetric in the entropic inner produc…
Time Step Expansions and the Invariant Manifold Approach to Lattice Boltzmann Models
David J. Packwood, Jeremy Levesley, Alexander N. Gorban
The classical method for deriving the macroscopic dynamics of a lattice Boltzmann system is to use a combination of different approximations and expansions. Usually a Chapman-Ensko…
Stable simulation of fluid flow with high-Reynolds number using Ehrenfests' steps
R. A. Brownlee, A. N. Gorban, J. Levesley
The Navier--Stokes equations arise naturally as a result of Ehrenfests' coarse-graining in phase space after a period of free-flight dynamics. This point of view allows for a very…
Nonequilibrium entropy limiters in lattice Boltzmann methods
R. A. Brownlee, A. N. Gorban, J. Levesley
We construct a system of nonequilibrium entropy limiters for the lattice Boltzmann methods (LBM). These limiters erase spurious oscillations without blurring of shocks, and do not…
Stabilisation of the lattice-Boltzmann method using the Ehrenfests' coarse-graining
R. A. Brownlee, A. N. Gorban, J. Levesley
The lattice-Boltzmann method (LBM) and its variants have emerged as promising, computationally efficient and increasingly popular numerical methods for modelling complex fluid flow…
Invariance correction to Grad's equations: Where to go beyond approximations?
A. N. Gorban, I. V. Karlin
We review some recent developments of Grad's approach to solving the Boltzmann equation and creating reduced description. The method of invariant manifold is put forward as a unifi…
Selection theorem for systems with inheritance
A. N. Gorban
The problem of finite-dimensional asymptotics of infinite-dimensional dynamic systems is studied. A non-linear kinetic system with conservation of supports for distributions has ge…
Geometry of irreversibility: The film of nonequilibrium states
A. N. Gorban, I. V. Karlin
A general geometrical framework of nonequilibrium thermodynamics is developed. The notion of macroscopically definable ensembles is developed. The thesis about macroscopically defi…
Methods of nonlinear kinetics
A. N. Gorban, I. V. Karlin
Nonlinear kinetic equations are reviewed for a wide audience of specialists and postgraduate students in physics, mathematical physics, material science, chemical engineering and i…
Quasi-Equilibrium Closure Hierarchies for The Boltzmann Equation
A. N. Gorban, I. V. Karlin
In this paper, explicit method of constructing approximations (the Triangle Entropy Method) is developed for nonequilibrium problems. This method enables one to treat any complicat…
The additive generalization of the Boltzmann entropy
Alexander N. Gorban, Iliya V. Karlin, Hans Christian Ottinger
There exists only one generalization of the classical Boltzmann-Gibbs-Shannon entropy functional to a one-parametric family of additive entropy functionals. We find analytical solu…
Hydrodynamics from Grad's equations: What can we learn from exact solutions?
Iliya V. Karlin, Alexander N. Gorban
A detailed treatment of the classical Chapman-Enskog derivation of hydrodynamics is given in the framework of Grad's moment equations. Grad's systems are considered as the minimal…
Family of additive entropy functions out of thermodynamic limit
Alexander N. Gorban, Iliya V. Karlin
Starting with the additivity condition for Lyapunov functions of master equation, we derive a one-parametric family of entropy functions which may be appropriate for a description…