THE THERMODYNAMIC DESCRIPTION OF HETEROGENEOUS DISSIPATIVE SYSTEMS BY VARIATIONAL METHODS: III. AN APPLICATION OF THE PRINCIPLE OF MINIMUM ENTROPY PRODUCTION TO FLUID DYNAMICS

1964 ◽  
Vol 42 (8) ◽  
pp. 1437-1446 ◽  
Author(s):  
J. S. Kirkaldy
Keyword(s):  
Steady State ◽  
Entropy Production ◽  
Thermodynamic Description ◽  
Free Fall ◽  
Dissipative Systems ◽  
Entropy Production Rate ◽  
Stable Steady State ◽  
Minimum Entropy ◽  
Minimum Entropy Production ◽  
Steady State Rate

The stable free-fall flight of a maple seed gives an exceptionally graphic demonstration of the principle of minimum entropy production. Since the rate of entropy production is proportional to the steady-state rate of loss of potential energy, it is visually obvious that the stable rotary configuration represents a minimum of the entropy production rate relative to an unstable steady-state bomblike trajectory. Regarding this phenomenon as the prototype of many practical steady-state fluid-dynamical systems involving rotational modes, we formally demonstrate the possibility of mathematically defining the stable steady-state configuration by means of this variational principle.

THE THERMODYNAMIC DESCRIPTION OF HETEROGENEOUS DISSIPATIVE SYSTEMS BY VARIATIONAL METHODS: IV. CONSEQUENCES OF A SYNTHESIS OF THE ONSAGER AND PRIGOGINE PRINCIPLES

1964 ◽  
Vol 42 (8) ◽  
pp. 1447-1454 ◽  
Author(s):  
J. S. Kirkaldy
Keyword(s):  
Steady State ◽  
Saddle Point ◽  
Entropy Production ◽  
Lagrange Equation ◽  
Thermodynamic Description ◽  
Metastable Equilibrium ◽  
Dissipative Systems ◽  
Stable Steady State ◽  
Reaction Products ◽  
Minimum Entropy

Since Onsager's steady-state dissipation principle and Prigogine's principle of minimum entropy production share a common Euler–Lagrange equation, their configuration spaces may be combined to form a single potential surface. As applied to phase transformations, the entropy production forms a saddle surface in the configuration space of possible stationary states. Those macroscopic variations which involve a change in morphology and a corresponding change in the thermodynamic forces during a spontaneous regression stabilize at a minimum of the entropy production (Prigogine's principle), whereas those microscopic variations, due to fluctuations of the fluxes with fixed forces and fixed morphology, stabilize at a maximum of the entropy production (Onsager's principle). A stable steady state is, therefore, defined by the saddle point.The internal constraints attending stationary phase transformation often exclude the saddle point as a possible state so that unstable configurations are obtained. Dendritic growth of alloy crystals is an example.Some isothermal eutectic or eutectoid reactions may be located at the saddle point. In this case the stabilization of the configuration against microscopic fluctuations requires that the reaction product be in metastable equilibrium. Alteration of the growth conditions may lead to macroscopic instability and a transition to a state lying off the saddle point. These systems evidence their instability by the roughly periodic form of the reaction products.

Computational Intelligence for Robust Control Algorithms of Complex Dynamic Systems with Minimum Entropy Production

1999 ◽  
Vol 3 (2) ◽  
pp. 82-98 ◽  
Author(s):  
S.V. Ulyanov ◽  
◽  
K. Yamafuji ◽  
V.S. Ulyanov ◽  
I. Kurawaki ◽  
...  
Keyword(s):  
Nonlinear Systems ◽  
Lyapunov Function ◽  
Entropy Production ◽  
Production Rate ◽  
Dynamic Systems ◽  
Fitness Function ◽  
Object Motion ◽  
Entropy Production Rate ◽  
Minimum Entropy ◽  
Minimum Entropy Production

Our thermodynamic approach to the study and design of robust optimal control processes in nonlinear (in general global unstable) dynamic systems used soft computing based on genetic algorithms with a fitness function as minimum entropy production. Control objects were nonlinear dynamic systems involving essentially nonlinear stochastic differential equations. An algorithm was developed for calculating entropy production rate in control object motion and in control systems. Part 1 discusses relation of the Lyapunov function (measure of stability) and the entropy production rate (physical measure of controllability). This relation was used to describe the following qualitative properties and important relations: dynamic stability motion (Lyapunov function), Lyapunov exponent and Kolmogorov-Sinai entropy, physical entropy production rates, and symmetries group representation in essentially nonlinear systems as coupled oscillator models. Results of computer simulation are presented for entropy-like dynamic behavior for typical benchmarks of dynamic systems such as Van der Pol, Duffing, and Holmes-Rand, and coupled oscillators. Parts 2 and 3 discuss the application of this approach to simulation of dynamic entropy-like behavior and optimal benchmark control as a 2-link manipulator in a robot for service use and nonlinear systems under stochastic excitation.

A New Criterion for Assessing Heat Exchanger Performance

2010 ◽  
Author(s):  
Jiangfeng Guo ◽  
Mingtian Xu ◽  
Lin Cheng
Keyword(s):  
Heat Exchanger ◽  
Entropy Production ◽  
Optimization Design ◽  
Rectangular Channel ◽  
Entropy Production Rate ◽  
Local Entropy ◽  
Minimum Entropy ◽  
Minimum Entropy Production ◽  
Production Distribution ◽  
New Criterion

The principle of minimum entropy production has played an important role in the development of non-equilibrium thermodynamics. Inspired by this principle, Bejan derived the expression of the local entropy production rate for heat convection and established the entropy production minimization approach for the heat exchanger optimization design. Although one can obtain the entropy production distribution in the heat exchanger numerically, it can not directly been employed to examine the heat exchanger performance. Tondeur and Kvaalen found that the entropy production uniformity is closely related to the heat exchanger performance. In the present work, based on Tondear and Kvaalen’s work, an entropy production uniformity factor is defined, which quantifies the uniformity of the local entropy generation distribution in heat exchanger. Numerical results of the heat transfer in a rectangular channel show that the larger entropy production uniformity factor implies less irreversible loses. Therefore, this factor can serve as a thermodynamic figure of merit for assessing the heat exchanger performance.

Irreversible Thermodynamic Description of Domain Occurrences in Ferroics

2012 ◽  
Vol 560-561 ◽  
pp. 140-144
Author(s):  
Yuan Zhen Cai
Keyword(s):  
Phase Transitions ◽  
Entropy Production ◽  
Stationary State ◽  
Thermodynamic Description ◽  
Irreversible Thermodynamic ◽  
Irreversible Thermodynamics ◽  
Minimum Entropy ◽  
Spatial Symmetry ◽  
Domain Structures ◽  
Minimum Entropy Production

Based on the irreversible thermodynamics, a irreversible thermodynamic description of domain occurrences in ferroics such as ferroelectrics, ferromagnetics and ferroelastics was given. The ferroic domain structures occur at the ferroic phase transitions from the prototype phases to the ferroic phases. The processes of transition are stationary state processes so that the principle of minimum entropy production is satisfied. The domain occurrences are a consequence of this principle. The time-spatial symmetry related to the domains and their occurrences was also expounded.

Thermodynamics of surface degradation, self-organization and self-healing for biomimetic surfaces

2009 ◽  
Vol 367 (1893) ◽  
pp. 1607-1627 ◽  
Author(s):  
Michael Nosonovsky ◽  
Bharat Bhushan
Keyword(s):  
Entropy Production ◽  
Excess Entropy ◽  
Self Organization ◽  
Entropy Production Rate ◽  
Self Healing ◽  
Minimum Entropy ◽  
Practical Applications ◽  
Biomimetic Surfaces ◽  
Minimum Entropy Production ◽  
Self Cleaning

Friction is a dissipative irreversible process; therefore, entropy is produced during frictional contact. The rate of entropy production can serve as a measure of degradation (e.g. wear). However, in many cases friction leads to self-organization at the surface. This is because the excess entropy is either driven away from the surface, or it is released at the nanoscale, while the mesoscale entropy decreases. As a result, the orderliness at the surface grows. Self-organization leads to surface secondary structures either due to the mutual adjustment of the contacting surfaces (e.g. by wear) or due to the formation of regular deformation patterns, such as friction-induced slip waves caused by dynamic instabilities. The effect has practical applications, since self-organization is usually beneficial because it leads to friction and wear reduction (minimum entropy production rate at the self-organized state). Self-organization is common in biological systems, including self-healing and self-cleaning surfaces. Therefore, designing a successful biomimetic surface requires an understanding of the thermodynamics of frictional self-organization. We suggest a multiscale decomposition of entropy and formulate a thermodynamic framework for irreversible degradation and for self-organization during friction. The criteria for self-organization due to dynamic instabilities are discussed, as well as the principles of biomimetic self-cleaning, self-lubricating and self-repairing surfaces by encapsulation and micro/nanopatterning.

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