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Actually this thermal "thermodynamic force" is a manifestation of the degree of inexact specification of the microscopic initial conditions for the system, expressed in the thermodynamic variable known as temperature, <math>T</math>. Temperature is only one example, and all the thermodynamic macroscopic variables constitute inexact specifications of the initial conditions, and have their respective "thermodynamic forces". These inexactitudes of specification are the source of the apparent fluctuations that drive the generation of dynamical structure, of the very precise but still less than perfect reproducibility of non-equilibrium experiments, and of the place of entropy in thermodynamics. If one did not know of such inexactitude of specification, one might find the origin of the fluctuations mysterious. What is meant here by "inexactitude of specification" is not that the mean values of the macroscopic variables are inexactly specified, but that the use of macroscopic variables to describe processes that actually occur by the motions and interactions of microscopic objects such as molecules is necessarily lacking in the molecular detail of the processes, and is thus inexact. There are many microscopic states compatible with a single macroscopic state, but only the latter is specified, and that is specified exactly for the purposes of the theory.

Actually this thermal "thermodynamic force" is a manifestation of the degree of inexact specification of the microscopic initial conditions for the system, expressed in the thermodynamic variable known as temperature, <math>T</math>. Temperature is only one example, and all the thermodynamic macroscopic variables constitute inexact specifications of the initial conditions, and have their respective "thermodynamic forces". These inexactitudes of specification are the source of the apparent fluctuations that drive the generation of dynamical structure, of the very precise but still less than perfect reproducibility of non-equilibrium experiments, and of the place of entropy in thermodynamics. If one did not know of such inexactitude of specification, one might find the origin of the fluctuations mysterious. What is meant here by "inexactitude of specification" is not that the mean values of the macroscopic variables are inexactly specified, but that the use of macroscopic variables to describe processes that actually occur by the motions and interactions of microscopic objects such as molecules is necessarily lacking in the molecular detail of the processes, and is thus inexact. There are many microscopic states compatible with a single macroscopic state, but only the latter is specified, and that is specified exactly for the purposes of the theory.

其实这种热 "热力 "是系统微观初始条件不精确规范程度的一种表现，用被称为温度的热力学变量<math>T</math>表示。温度只是一个例子，所有的热力学宏观变量都构成了初始条件的不精确规格，都有各自的 "热力学力"。这些不精确的规格是推动动力结构产生的明显波动的根源，是非平衡实验非常精确但仍不太完美的重复性的根源，也是熵在热力学中的地位的根源。如果不知道这种不精确的规范，人们可能会觉得波动的起源很神秘。这里所说的 "规范的不精确性"，并不是说宏观变量的均值规定得不精确，而是说用宏观变量来描述分子等微观物体的运动和相互作用实际发生的过程，必然缺乏过程的分子细节，因而不精确。有许多微观状态与单一的宏观状态相适应，但只有后者被规定，而这正是为了理论的目的而规定的。

其实这种"热力学力"是系统微观初始条件不精确程度的一种表现，用被称为温度的热力学变量<math>T</math>表示。温度只是一个例子，所有的热力学宏观变量都构成了初始条件的不精确规格，都有各自的 "热力学力"。这些不精确的规格是推动动力结构产生明显波动的根源，是非平衡实验非常精确但仍不太完美的重复性的根源，也是熵在热力学中的地位的根源。如果不知道这种不精确的规格，人们可能会觉得波动的起源很神秘。这里所说的 "规格的不精确性"，并不是说宏观变量的均值规定得不精确，而是说用宏观变量来描述分子等微观物体的运动和相互作用实际发生的过程，必然缺乏过程的分子细节，因而不精确。有许多微观状态与单一的宏观状态相适应，但只有后者被规定，而这正是为了理论的目的而规定的。

It is reproducibility in repeated observations that identifies dynamical structure in a system. [[Edwin Thompson Jaynes|E.T. Jaynes]]<ref name="Jaynes 1957 I">{{cite journal | last1 = Jaynes | first1 = E.T. | year = 1957 | title = Information theory and statistical mechanics | url = http://bayes.wustl.edu/etj/articles/theory.1.pdf | journal = Physical Review | volume = 106 | issue = 4| pages = 620–630 | doi=10.1103/physrev.106.620| bibcode = 1957PhRv..106..620J }}</ref><ref name="Jaynes 1957 II">{{cite journal | last1 = Jaynes | first1 = E.T. | year = 1957 | title = Information theory and statistical mechanics. II | url = http://bayes.wustl.edu/etj/articles/theory.2.pdf | journal = Physical Review | volume = 108 | issue = 2| pages = 171–190 | doi=10.1103/physrev.108.171| bibcode = 1957PhRv..108..171J }}</ref><ref name="Jaynes 1985">[http://bayes.wustl.edu/etj/articles/macroscopic.prediction.pdf Jaynes, E.T. (1985). Macroscopic prediction, in ''Complex Systems - Operational Approaches in Neurobiology'', edited by H. Haken, Springer-Verlag, Berlin, pp. 254-269] {{ISBN|3-540-15923-1}}.</ref><ref name="Jaynes 1965">{{cite journal | last1 = Jaynes | first1 = E.T. | year = 1965 | title = Gibbs vs Boltzmann Entropies | url = http://bayes.wustl.edu/etj/articles/gibbs.vs.boltzmann.pdf | journal = American Journal of Physics | volume = 33 | issue = 5| pages = 391–398 | doi=10.1119/1.1971557| bibcode = 1965AmJPh..33..391J }}</ref> explains how this reproducibility is why entropy is so important in this topic: entropy is a measure of experimental reproducibility. The entropy tells how many times one would have to repeat the experiment in order to expect to see a departure from the usual reproducible result. When the process goes on in a system with less than a 'practically infinite' number (much much less than Avogadro's or Loschmidt's numbers) of molecules, the thermodynamic reproducibility fades, and fluctuations become easier to see.<ref name="Evans Searles 2002">{{cite journal | last1 = Evans | first1 = D.J. | last2 = Searles | first2 = D.J. | s2cid = 10308868 | year = 2002 | title = The fluctuation theorem | journal = Advances in Physics | volume = 51 | issue = 7| pages = 1529–1585 | doi=10.1080/00018730210155133| bibcode = 2002AdPhy..51.1529E }}</ref><ref name="WSMSE 2002">Wang, G.M., Sevick, E.M., Mittag, E., Searles, D.J., Evans, D.J. (2002) Experimental demonstration of violations of the Second Law of Thermodynamics for small systems and short time scales, ''Physical Review Letters'' 89: 050601-1 - 050601-4.</ref>

It is reproducibility in repeated observations that identifies dynamical structure in a system. [[Edwin Thompson Jaynes|E.T. Jaynes]]<ref name="Jaynes 1957 I">{{cite journal | last1 = Jaynes | first1 = E.T. | year = 1957 | title = Information theory and statistical mechanics | url = http://bayes.wustl.edu/etj/articles/theory.1.pdf | journal = Physical Review | volume = 106 | issue = 4| pages = 620–630 | doi=10.1103/physrev.106.620| bibcode = 1957PhRv..106..620J }}</ref><ref name="Jaynes 1957 II">{{cite journal | last1 = Jaynes | first1 = E.T. | year = 1957 | title = Information theory and statistical mechanics. II | url = http://bayes.wustl.edu/etj/articles/theory.2.pdf | journal = Physical Review | volume = 108 | issue = 2| pages = 171–190 | doi=10.1103/physrev.108.171| bibcode = 1957PhRv..108..171J }}</ref><ref name="Jaynes 1985">[http://bayes.wustl.edu/etj/articles/macroscopic.prediction.pdf Jaynes, E.T. (1985). Macroscopic prediction, in ''Complex Systems - Operational Approaches in Neurobiology'', edited by H. Haken, Springer-Verlag, Berlin, pp. 254-269] {{ISBN|3-540-15923-1}}.</ref><ref name="Jaynes 1965">{{cite journal | last1 = Jaynes | first1 = E.T. | year = 1965 | title = Gibbs vs Boltzmann Entropies | url = http://bayes.wustl.edu/etj/articles/gibbs.vs.boltzmann.pdf | journal = American Journal of Physics | volume = 33 | issue = 5| pages = 391–398 | doi=10.1119/1.1971557| bibcode = 1965AmJPh..33..391J }}</ref> explains how this reproducibility is why entropy is so important in this topic: entropy is a measure of experimental reproducibility. The entropy tells how many times one would have to repeat the experiment in order to expect to see a departure from the usual reproducible result. When the process goes on in a system with less than a 'practically infinite' number (much much less than Avogadro's or Loschmidt's numbers) of molecules, the thermodynamic reproducibility fades, and fluctuations become easier to see.<ref name="Evans Searles 2002">{{cite journal | last1 = Evans | first1 = D.J. | last2 = Searles | first2 = D.J. | s2cid = 10308868 | year = 2002 | title = The fluctuation theorem | journal = Advances in Physics | volume = 51 | issue = 7| pages = 1529–1585 | doi=10.1080/00018730210155133| bibcode = 2002AdPhy..51.1529E }}</ref><ref name="WSMSE 2002">Wang, G.M., Sevick, E.M., Mittag, E., Searles, D.J., Evans, D.J. (2002) Experimental demonstration of violations of the Second Law of Thermodynamics for small systems and short time scales, ''Physical Review Letters'' 89: 050601-1 - 050601-4.</ref>

It is reproducibility in repeated observations that identifies dynamical structure in a system. E.T. Jaynes explains how this reproducibility is why entropy is so important in this topic: entropy is a measure of experimental reproducibility. The entropy tells how many times one would have to repeat the experiment in order to expect to see a departure from the usual reproducible result. When the process goes on in a system with less than a 'practically infinite' number (much much less than Avogadro's or Loschmidt's numbers) of molecules, the thermodynamic reproducibility fades, and fluctuations become easier to see.

It is reproducibility in repeated observations that identifies dynamical structure in a system. E.T. Jaynes explains how this reproducibility is why entropy is so important in this topic: entropy is a measure of experimental reproducibility. The entropy tells how many times one would have to repeat the experiment in order to expect to see a departure from the usual reproducible result. When the process goes on in a system with less than a 'practically infinite' number (much much less than Avogadro's or Loschmidt's numbers) of molecules, the thermodynamic reproducibility fades, and fluctuations become easier to see.

正是重复观测中的可重复性确定了系统中的动态结构。E.T.杰恩斯E.T.Jaynes解释了这种可重复性是如何在这个主题中熵如此重要的原因：熵是实验可重复性的衡量标准。熵告诉人们要重复多少次实验才能期望看到与通常的可重复性结果相背离。当这个过程在一个分子数量少于 "几乎无限 "的系统中进行时（比阿伏加德罗或洛施密特的数量少得多），热力学的可重复性就会减弱，波动就会变得更容易看到。

正是重复观测中的可重复性确定了系统中的动态结构。E.T.杰恩斯E.T.Jaynes 解释了这种可重复性是如何解释熵在这个主题中如此重要的原因:熵是实验可重复性的衡量标准。熵告诉人们要重复多少次实验才能期望看到一个偏离通常可重复的结果。当这个过程在一个分子数量少于 "几乎无限 "的系统中进行时（比阿伏加德罗或洛施密特的数量少得多），热力学的可重复性就会减弱，波动就会变得更容易看到。

According to this view of [[Edwin Thompson Jaynes|Jaynes]], it is a common and mystificatory abuse of language, that one often sees reproducibility of dynamical structure called "order".<ref name="Grandy 2008"/><ref name="Dewar 2005">Dewar, R.C. (2005). Maximum entropy production and non-equilibrium statistical mechanics, pp. 41-55 in ''Non-equilibrium Thermodynamics and the Production of Entropy'', edited by A. Kleidon, R.D. Lorenz, Springer, Berlin. {{ISBN|3-540-22495-5}}.</ref> Dewar<ref name="Dewar 2005"/> writes "Jaynes considered reproducibility - rather than disorder -  to be the key idea behind the second law of thermodynamics (Jaynes 1963,<ref name="Jaynes 1963">[http://bayes.wustl.edu/etj/articles/brandeis.pdf Jaynes, E.T. (1963). pp. 181-218 in ''Brandeis Summer Institute 1962, Statistical Physics'', edited by K.W. Ford, Benjamin, New York.]</ref> 1965,<ref name="Jaynes 1965"/> 1988,<ref name="Jaynes 1988">[http://bayes.wustl.edu/etj/articles/ccarnot.pdf Jaynes, E.T. (1988). The evolution of Carnot's Principle, pp. 267-282 in ''Maximum-entropy and Bayesian methods in science and engineering'', edited by G.J. Erickson, C.R. Smith, Kluwer, Dordrecht, volume 1] {{ISBN|90-277-2793-7}}.</ref> 1989<ref name="Jaynes 1989">[http://bayes.wustl.edu/etj/articles/cmystery.pdf Jaynes, E.T. (1989). Clearing up mysteries, the original goal, pp. 1-27 in ''Maximum entropy and Bayesian methods'', Kluwer, Dordrecht.]</ref>)." Grandy (2008)<ref name="Grandy 2008"/> in section 4.3 on page 55 clarifies the distinction between the idea that entropy is related to order (which he considers to be an "unfortunate" "mischaracterization" that needs "debunking"), and the aforementioned idea of [[Edwin Thompson Jaynes|Jaynes]] that entropy is a measure of experimental reproducibility of process (which Grandy regards as correct). According to this view, even the admirable book of Glansdorff and Prigogine (1971)<ref name="G&P 1971"/> is guilty of this unfortunate abuse of language.

According to this view of [[Edwin Thompson Jaynes|Jaynes]], it is a common and mystificatory abuse of language, that one often sees reproducibility of dynamical structure called "order".<ref name="Grandy 2008"/><ref name="Dewar 2005">Dewar, R.C. (2005). Maximum entropy production and non-equilibrium statistical mechanics, pp. 41-55 in ''Non-equilibrium Thermodynamics and the Production of Entropy'', edited by A. Kleidon, R.D. Lorenz, Springer, Berlin. {{ISBN|3-540-22495-5}}.</ref> Dewar<ref name="Dewar 2005"/> writes "Jaynes considered reproducibility - rather than disorder -  to be the key idea behind the second law of thermodynamics (Jaynes 1963,<ref name="Jaynes 1963">[http://bayes.wustl.edu/etj/articles/brandeis.pdf Jaynes, E.T. (1963). pp. 181-218 in ''Brandeis Summer Institute 1962, Statistical Physics'', edited by K.W. Ford, Benjamin, New York.]</ref> 1965,<ref name="Jaynes 1965"/> 1988,<ref name="Jaynes 1988">[http://bayes.wustl.edu/etj/articles/ccarnot.pdf Jaynes, E.T. (1988). The evolution of Carnot's Principle, pp. 267-282 in ''Maximum-entropy and Bayesian methods in science and engineering'', edited by G.J. Erickson, C.R. Smith, Kluwer, Dordrecht, volume 1] {{ISBN|90-277-2793-7}}.</ref> 1989<ref name="Jaynes 1989">[http://bayes.wustl.edu/etj/articles/cmystery.pdf Jaynes, E.T. (1989). Clearing up mysteries, the original goal, pp. 1-27 in ''Maximum entropy and Bayesian methods'', Kluwer, Dordrecht.]</ref>)." Grandy (2008)<ref name="Grandy 2008"/> in section 4.3 on page 55 clarifies the distinction between the idea that entropy is related to order (which he considers to be an "unfortunate" "mischaracterization" that needs "debunking"), and the aforementioned idea of [[Edwin Thompson Jaynes|Jaynes]] that entropy is a measure of experimental reproducibility of process (which Grandy regards as correct). According to this view, even the admirable book of Glansdorff and Prigogine (1971)<ref name="G&P 1971"/> is guilty of this unfortunate abuse of language.

According to this view of Jaynes, it is a common and mystificatory abuse of language, that one often sees reproducibility of dynamical structure called "order". Dewar "Jaynes considered reproducibility - rather than disorder - to be the key idea behind the second law of thermodynamics (Jaynes 1963,1965,1988,1989)." Grandy (2008) in section 4.3 on page 55 clarifies the distinction between the idea that entropy is related to order (which he considers to be an "unfortunate" "mischaracterization" that needs "debunking"), and the aforementioned idea of Jaynes that entropy is a measure of experimental reproducibility of process (which Grandy regards as correct). According to this view, even the admirable book of Glansdorff and Prigogine (1971)is guilty of this unfortunate abuse of language.

According to this view of Jaynes, it is a common and mystificatory abuse of language, that one often sees reproducibility of dynamical structure called "order". Dewar "Jaynes considered reproducibility - rather than disorder - to be the key idea behind the second law of thermodynamics (Jaynes 1963,1965,1988,1989)." Grandy (2008) in section 4.3 on page 55 clarifies the distinction between the idea that entropy is related to order (which he considers to be an "unfortunate" "mischaracterization" that needs "debunking"), and the aforementioned idea of Jaynes that entropy is a measure of experimental reproducibility of process (which Grandy regards as correct). According to this view, even the admirable book of Glansdorff and Prigogine (1971)is guilty of this unfortunate abuse of language.

根据Jaynes的这一观点，人们经常看到动态结构的可重复性被称为 "秩序"，这是一种常见的、神秘化的语言滥用。杜瓦 Dewar 写道"Jaynes将可重复性而不是无序性视为是热力学第二定律背后的关键思想（Jaynes1963,1965,1988,1989）"。格兰迪Grandy(2008)在第55页4.3节中阐明了熵与秩序有关的观点之间的区别(他认为熵与秩序有关这是一种 "不幸的""错误描述"，需要 "揭穿")，以及Jaynes的上述观点，即熵是实验过程可重复性的衡量标准(格兰迪认为这是正确的)。按照这种观点，即使是《Glandsdorff和Prigogine》(1971)这本令人钦佩的书也犯了这种不幸的滥用语言的毛病。

根据Jaynes的这一观点，人们经常看到动态结构的可重复性被称为 "秩序"，这是一种常见的、神秘化的语言滥用。杜瓦 Dewar 写道"Jaynes将可重复性而不是无序性视为是热力学第二定律背后的关键思想（Jaynes1963,1965,1988,1989）"。格兰迪Grandy(2008)在第55页4.3节中阐明了熵与秩序有关的观点之间的区别(他认为熵与秩序有关这是一种 "不幸的""错误描述"，需要 "被揭穿")，以及Jaynes的上述观点，即熵是实验过程可重复性的衡量标准(格兰迪认为这是正确的)。按照这种观点，即使是《Glandsdorff和Prigogine》(1971)这本令人钦佩的书也犯了这种不幸的滥用语言的毛病。

==Local thermodynamic equilibrium==

==Local thermodynamic equilibrium==