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第380行： − + − + + − Until recently, prospects for useful extremal principles in this area have seemed clouded. Nicolis (1999)<ref>{{Cite journal | doi = 10.1002/qj.49712555718 | last1 = Nicolis | first1 = C. | year = 1999 | title = Entropy production and dynamical complexity in a low-order atmospheric model | url = | journal = Quarterly Journal of the Royal Meteorological Society | volume = 125 | issue = 557| pages = 1859–1878 |bibcode = 1999QJRMS.125.1859N }}</ref> concludes that one model of atmospheric dynamics has an attractor which is not a regime of maximum or minimum dissipation; she says this seems to rule out the existence of a global organizing principle, and comments that this is to some extent disappointing; she also points to the difficulty of finding a thermodynamically consistent form of entropy production. Another top expert offers an extensive discussion of the possibilities for principles of extrema of entropy production and of dissipation of energy: Chapter 12 of Grandy (2008)<ref name="Grandy 2008"/> is very cautious, and finds difficulty in defining the 'rate of internal entropy production' in many cases, and finds that sometimes for the prediction of the course of a process, an extremum of the quantity called the rate of dissipation of energy may be more useful than that of the rate of entropy production; this quantity appeared in Onsager's 1931<ref name="Onsager 1931 I"/> origination of this subject. Other writers have also felt that prospects for general global extremal principles are clouded. Such writers include Glansdorff and Prigogine (1971), Lebon, Jou and Casas-Vásquez (2008), and Šilhavý (1997). − There is good experimental evidence that heat convection does not obey extremal principles for time rate of entropy production.<ref name="Attard 2012">{{cite arXiv|last=Attard|first=P.|title=Optimising Principle for Non-Equilibrium Phase Transitions and Pattern Formation with Results for Heat Convection|journal=|year=2012|eprint=1208.5105|class=cond-mat.stat-mech}}</ref> Theoretical analysis shows that chemical reactions do not obey extremal principles for the second differential of time rate of entropy production.<ref name="Keizer 1974">{{cite journal |last1=Keizer |first1=J. |last2=Fox |first2=R. |date=January 1974 |title=Qualms Regarding the Range of Validity of the Glansdorff-Prigogine Criterion for Stability of Non-Equilibrium States |journal=PNAS |volume=71 |pages=192–196 |doi=10.1073/pnas.71.1.192|pmid=16592132 }}</ref> The development of a general extremal principle seems infeasible in the current state of knowledge. + +
→Speculated extremal principles for non-equilibrium processes
Pokrovskii给出了上述熵产生速率方程的广义概括。
Pokrovskii给出了上述熵产生速率方程的广义概括。
==Speculated extremal principles for non-equilibrium processes==
== Speculated extremal principles for non-equilibrium processes 非平衡过程的推测极值原理 ==
{{main|Extremal principles in non-equilibrium thermodynamics}}
{{main|Extremal principles in non-equilibrium thermodynamics}}
Until recently, prospects for useful extremal principles in this area have seemed clouded. Nicolis (1999)<ref>{{Cite journal | doi = 10.1002/qj.49712555718 | last1 = Nicolis | first1 = C. | year = 1999 | title = Entropy production and dynamical complexity in a low-order atmospheric model | journal = Quarterly Journal of the Royal Meteorological Society | volume = 125 | issue = 557| pages = 1859–1878 |bibcode = 1999QJRMS.125.1859N }}</ref> concludes that one model of atmospheric dynamics has an attractor which is not a regime of maximum or minimum dissipation; she says this seems to rule out the existence of a global organizing principle, and comments that this is to some extent disappointing; she also points to the difficulty of finding a thermodynamically consistent form of entropy production. Another top expert offers an extensive discussion of the possibilities for principles of extrema of entropy production and of dissipation of energy: Chapter 12 of Grandy (2008)<ref name="Grandy 2008"/> is very cautious, and finds difficulty in defining the 'rate of internal entropy production' in many cases, and finds that sometimes for the prediction of the course of a process, an extremum of the quantity called the rate of dissipation of energy may be more useful than that of the rate of entropy production; this quantity appeared in Onsager's 1931<ref name="Onsager 1931 I"/> origination of this subject. Other writers have also felt that prospects for general global extremal principles are clouded. Such writers include Glansdorff and Prigogine (1971), Lebon, Jou and Casas-Vásquez (2008), and Šilhavý (1997).
即使发展到现在，其相关领域中，具有运用价值的极值理论仍然很模糊。Nicolis尼科利斯（1999）总结认为，一种大气动力学模型具有一个吸引子，并且该吸引子不处于最大或最小耗散状态。她说，这似乎排除了全局组织原则的存在，并评论说这个结论在某种程度上令人失望；她还指出了寻找熵产生的热力学通用形式相当困难。另一位顶级专家则广泛讨论了熵的产生和能量耗散的极值原理：格兰迪Grandy（2008）在他的文章第12节（待确定）非常谨慎地提出，在许多情况下，很难定义“内部熵产生的速率”，并且发现有时为了预测过程，将数量的极值称为速率能量耗散极值可能比熵产生速率极值有用。这个数量曾经出现在Onsager于1931年提出相关论点中。同时其他作者也感到，广义的全局极值原理前景不太明朗。这类作家包括Glansdorff和Prigogine（1971），Lebon，Jou和Casas-Vásquez（2008）和Šilhavý（1997）。
There is good experimental evidence that heat convection does not obey extremal principles for time rate of entropy production.<ref name="Attard 2012">{{cite arXiv|last=Attard|first=P.|title=Optimising Principle for Non-Equilibrium Phase Transitions and Pattern Formation with Results for Heat Convection|year=2012|eprint=1208.5105|class=cond-mat.stat-mech}}</ref> Theoretical analysis shows that chemical reactions do not obey extremal principles for the second differential of time rate of entropy production.<ref name="Keizer 1974">{{cite journal |last1=Keizer |first1=J. |last2=Fox |first2=R. |date=January 1974 |title=Qualms Regarding the Range of Validity of the Glansdorff-Prigogine Criterion for Stability of Non-Equilibrium States |journal=PNAS |volume=71 |pages=192–196 |doi=10.1073/pnas.71.1.192|pmid=16592132 }}</ref> The development of a general extremal principle seems infeasible in the current state of knowledge.
有充分的实验证据表明，热对流不符合熵产生时间速率的极值原理。理论分析表明，化学反应没有遵循熵产生时间速率的二次微分极值原理，以目前的知识体系，一般性极值原理的发展似乎是不可行的。
==Applications==
==Applications==