title: Modelling non-equilibrium thermodynamic systems from the speed-gradient principle.
abstract: The application of the speed-gradient (SG) principle to the non-equilibrium distribution systems far away from thermodynamic equilibrium is investigated. The options for applying the SG principle to describe the non-equilibrium transport processes in real-world environments are discussed. Investigation of a non-equilibrium system's evolution at different scale levels via the SG principle allows for a fresh look at the thermodynamics problems associated with the behaviour of the system entropy. Generalized dynamic equations for finite and infinite number of constraints are proposed. It is shown that the stationary solution to the equations, resulting from the SG principle, entirely coincides with the locally equilibrium distribution function obtained by Zubarev. A new approach to describe time evolution of systems far from equilibrium is proposed based on application of the SG principle at the intermediate scale level of the system's internal structure. The problem of the high-rate shear flow of viscous fluid near the rigid plane plate is discussed. It is shown that the SG principle allows closed mathematical models of non-equilibrium processes to be constructed.This article is part of the themed issue 'Horizons of cybernetical physics'.
authors.affiliation: Mathematics and Mechanics Faculty, Saint-Petersburg State University, Saint-Petersburg, Russia.|The Laboratory 'Control of Complex Systems', Institute of Problems of Mechanical Engineering RAS, Saint-Petersburg, Russia.
authors.forename: Tatiana A
authors.initials: TA
authors.lastname: Khantuleva
authors.affiliation: Mathematics and Mechanics Faculty, Saint-Petersburg State University, Saint-Petersburg, Russia dmitry.shalymov@gmail.com.|The Laboratory 'Control of Complex Systems', Institute of Problems of Mechanical Engineering RAS, Saint-Petersburg, Russia.
authors.forename: Dmitry S
authors.identifier: http://orcid.org/0000-0002-8794-7306
authors.initials: DS
authors.lastname: Shalymov
keywords: differential entropy; maximum entropy principle; speed-gradient principle