speed-gradient entropy principle for nonstationary processes速度梯度为非平稳过程熵原理.pdfVIP

Entropy 2008, 10, 757-764; DOI: 10.3390/ OPEN ACCESS entropy ISSN 1099-4300 /journal/entropy Article Speed-gradient Entropy Principle for Nonstationary Processes Alexander Fradkov Institute for Problems of Mechanical Engineering, Russian Academy of Sciences, 61, Bolshoy ave. V.O., 199178, Saint Petersburg, Russia. E-mail: fradkov@mail.ru Received: 24 May 2008 / Accepted: 1 December 2008 / Published: 8 December 2008 Abstract: The speed-gradient variational principle (SG-principle) for nonstationary far from equilibrium systems is formulated and illustrated by examples. The SG-model of transient (relaxation) dynamics for systems of a finite number of particles based on maximum entropy principle is derived. It has the form where is the vector of the cell populations, is a symmetric matrix with two zero eigenvalues corresponding to mass and energy conservation laws. Keywords: Nonequilibrium thermodynamics, variational principles, Maximum Entropy Prin- ciple. 1. Introduction The equations of motion for physical systems are often derived from variational principles: principle of least action, maximum entropy principle, etc. [1–4]. Variational principles are based on specification of a functional (usually, integral functional) and determination of real motions as points in an appropriate functional space providing extrema of the specified functional. The principle is called integral if the functional to be extremized has an integral form. In addition to integral principles, differential (local) ones were