Khantuleva Tatiana A, Shalymov Dmitry S
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.
Philos Trans A Math Phys Eng Sci. 2017 Mar 6;375(2088). doi: 10.1098/rsta.2016.0220.
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'.
研究了速度梯度（SG）原理在远离热力学平衡的非平衡分布系统中的应用。讨论了应用SG原理描述现实环境中非平衡传输过程的各种选择。通过SG原理对非平衡系统在不同尺度水平上的演化进行研究，有助于重新审视与系统熵行为相关的热力学问题。提出了有限和无限数量约束的广义动力学方程。结果表明，由SG原理得出的方程的稳态解与祖巴列夫获得的局部平衡分布函数完全一致。基于在系统内部结构的中间尺度水平上应用SG原理，提出了一种描述远离平衡系统时间演化的新方法。讨论了粘性流体在刚性平板附近的高速剪切流问题。结果表明，SG原理允许构建非平衡过程的封闭数学模型。本文是主题为“控制论物理学的前沿”特刊的一部分。
