Internal control in nonequilibrium transport

Хантулева, Т. А.

doi:10.1109/phycon.2005.1513947

Cited by 4 publications

(12 citation statements)

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“…SG-principle suggests that the transient behavior is potential with respect to the rate of some goal function. This idea may be applied also to evaluation of nonequilibrium stationary states and study of system internal structure evolution [17], description of transient slow motions in vibrational mechanics, etc. A different approach to variational description of nonstationary nonequilibrium processes is proposed in [18].…”

Section: Discussionmentioning

confidence: 99%

Speed-gradient Entropy Principle for Nonstationary Processes

Fradkov

2008

Entropy

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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 dX(t)/dt = A ln X(t), where X(t) is the vector of the cell populations, A is a symmetric matrix with two zero eigenvalues corresponding to mass and energy conservation laws.

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Section: Discussionmentioning

confidence: 99%

Speed-gradient Entropy Principle for Nonstationary Processes

Fradkov

2008

Entropy

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“…The rate of the structure evolution can change and lead to structure transitions with switching from one mode to another. The appearing feedback form the internal control closed-loops [23,24].…”

Section: Special Features Of Non-equilibrium Processesmentioning

confidence: 99%

“…To overcome these difficulties and to develop macroscopic description of non-equilibrium processes outside the framework of the conventional hydrodynamic stage close to the local equilibrium, a new approach based on the integral thermodynamic relationships is proposed [23][24][25][26]. Unlike the papers [1][2][3][4]7], where the problem of the irreversibility is considered at two-scale levels (macroscopic and microscopic), a third-scale level, intermediate between macroscopic and microscopic levels, is introduced.…”

Section: Introductionmentioning

confidence: 99%

“…The new level, called mesoscopic, is determined by the first moments of the spatio-temporal correlation function in the generalized thermodynamic relationships obtained by Zubarev. As shown in papers [23][24][25][26], the spatial moments are connected to the size of new internal structure of the system and the temporal ones correspond to the living time of the structure. Experimental data [27] show that the external action, deflecting the system state far from equilibrium, gives rise to self-organization making the system structured.…”

Section: Introductionmentioning

confidence: 99%

“…This universality allows the SG principle to build a closed mathematical model of non-equilibrium processes with feedback between the evolution of the internal structure of the system and its macroscopic response to an external perturbation. The approach based on the results of Zubarev and the SG principle is investigated in [23][24][25][26]. Applying this approach to the description of the shock-wave transient processes in condensed matter showed that it can be used to describe some of the detected anomalous effects, which do not find their explanation in the framework of traditional mechanical models [31][32][33].…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Modelling non-equilibrium thermodynamic systems from the speed-gradient principle

Хантулева

Shalymov

2017

Phil. Trans. R. Soc. A.

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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'.

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Dynamics of the Group Entropy Maximization Processes and of the Relative Entropy Group Minimization Processes Based on theSpeed‐gradient Principle

Preda¹,

Băncescu²

2020

Statistical Topics and Stochastic Models for Dependent Data With Applications

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Internal control in nonequilibrium transport

Cited by 4 publications

References 4 publications

Speed-gradient Entropy Principle for Nonstationary Processes

Speed-gradient Entropy Principle for Nonstationary Processes

Modelling non-equilibrium thermodynamic systems from the speed-gradient principle

Dynamics of the Group Entropy Maximization Processes and of the Relative Entropy Group Minimization Processes Based on theSpeed‐gradient Principle

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