961
个编辑
更改
跳到导航
跳到搜索
第212行：
第212行： − + − This point of view shares many points in common with the concept and the use of entropy in continuum thermomechanics, which evolved completely independently of statistical mechanics and maximum-entropy principles.+ − − 这种观点与连续热力学中熵的概念和使用有许多共同点，连续热力学完全独立于统计力学和最大熵原理演化。 − The scope of present-day non-equilibrium thermodynamics does not cover all physical processes. A condition for the validity of many studies in non-equilibrium thermodynamics of matter is that they deal with what is known as ''local thermodynamic equilibrium''.+ − + − To describe deviation of the thermodynamic system from equilibrium, in addition to constitutive variables <math>x_1, x_2, ..., x_n</math> that are used to fix the equilibrium state, as was described above, a set of variables <math>\xi_1, \xi_2,\ldots</math> that are called internal variables have been introduced. The equilibrium state is considered to be stable and the main property of the internal variables, as measures of non-equilibrium of the system, is their trending to disappear; the local law of disappearing can be written as relaxation equation for each internal variable+ − 为了描述热力学系统偏离平衡状态的程度，除了用于确定平衡状态的本构变量 x _ 1，x _ 2，... ，x _ n </math > 之外，还引入了一组称为内部变量的变量 x _ 1，x _ 2，ldots </math > 。平衡态被认为是稳定的，内变量作为系统非平衡的度量，其主要性质是它们趋于消失，消失的局部规律可以写成每个内变量的松弛方程 − − − {{NumBlk|:|<math> − − {{ NumBlk | : | < math > − \frac{d\xi_i}{dt} = - \frac{1}{\tau_i} \, \left(\xi_i - \xi_i^{(0)} \right),\quad i =1,\,2,\ldots , + − − 1} ，左(xi-xi-xi _ i ^ {(0)}右) ，quad i = 1，，2，ldots, − − − − </math>|}} − [/math > | } − ===Milne's definition in terms of radiative equilibrium=== − where <math> \tau_i= \tau_i(T, x_1, x_2, \ldots, x_n)</math> is a relaxation time of a corresponding variables. It is convenient to consider the initial value <math> \xi_i^0</math> are equal to zero. The above equation is valid for small deviations from equilibrium; The dynamics of internal variables in general case is considered by Pokrovskii.+ − − 其中 < math > tau _ i = tau _ i (t，x _ 1，x _ 2，ldots，x _ n) </math > 是对应变量的松弛时间。考虑初始值 < math > xi _ i ^ 0 </math > 等于零是很方便的。上述方程适用于小偏离均衡的情况，Pokrovskii 考虑了一般情况下内变量的动力学。 − + − − Entropy of the system in non-equilibrium is a function of the total set of variables − − 非平衡态系统的熵是总变量集的函数
→Local thermodynamic equilibrium
如果静态反应过程是不稳定的，那么任何波动都很大概率会触发系统从不稳定的静止状态下产生爆炸，并伴随着熵输出的增加。
如果静态反应过程是不稳定的，那么任何波动都很大概率会触发系统从不稳定的静止状态下产生爆炸，并伴随着熵输出的增加。
==Local thermodynamic equilibrium==
== Local thermodynamic equilibrium 局部热力学平衡 ==
The scope of present-day non-equilibrium thermodynamics does not cover all physical processes. A condition for the validity of many studies in non-equilibrium thermodynamics of matter is that they deal with what is known as ''local thermodynamic equilibrium''.
当今非平衡热力学的范围并不涵盖所有物理过程。在物质的非平衡热力学中有许多研究有效性的条件是：他们与所谓的局部热力学平衡相关。
===Ponderable matter===
=== Ponderable matter 疑难杂症===
''Local thermodynamic equilibrium of matter''<ref name="Gyarmati 1970"/><ref name="G&P 1971"/><ref name="Balescu 1975"/><ref name="Mihalas Mihalas 1984"/><ref name="Schloegl 1989"/> (see also Keizer (1987)<ref name="Keizer 1987"/> means that conceptually, for study and analysis, the system can be spatially and temporally divided into 'cells' or 'micro-phases' of small (infinitesimal) size, in which classical thermodynamical equilibrium conditions for matter are fulfilled to good approximation. These conditions are unfulfilled, for example, in very rarefied gases, in which molecular collisions are infrequent; and in the boundary layers of a star, where radiation is passing energy to space; and for interacting fermions at very low temperature, where dissipative processes become ineffective. When these 'cells' are defined, one admits that matter and energy may pass freely between contiguous 'cells', slowly enough to leave the 'cells' in their respective individual local thermodynamic equilibria with respect to intensive variables.
''Local thermodynamic equilibrium of matter''<ref name="Gyarmati 1970"/><ref name="G&P 1971"/><ref name="Balescu 1975"/><ref name="Mihalas Mihalas 1984"/><ref name="Schloegl 1989"/> (see also Keizer (1987)<ref name="Keizer 1987"/> means that conceptually, for study and analysis, the system can be spatially and temporally divided into 'cells' or 'micro-phases' of small (infinitesimal) size, in which classical thermodynamical equilibrium conditions for matter are fulfilled to good approximation. These conditions are unfulfilled, for example, in very rarefied gases, in which molecular collisions are infrequent; and in the boundary layers of a star, where radiation is passing energy to space; and for interacting fermions at very low temperature, where dissipative processes become ineffective. When these 'cells' are defined, one admits that matter and energy may pass freely between contiguous 'cells', slowly enough to leave the 'cells' in their respective individual local thermodynamic equilibria with respect to intensive variables.
从概念上讲，为了进行研究和分析，物质的局部热力学平衡（另请参见Keizer（1987）可以假设系统在空间和时间上划分为小尺寸（无穷小）的“细胞”或“微相”，那么其中物质的经典热力学平衡条件就能很好地满足。但是仍然存在某些条件无法得到满足，例如在极稀有的气体中，很少会发生分子碰撞；在恒星的边界层，辐射将能量传递到太空；以及在很低的温度下，与费米子的相互作用（其耗散过程变得无效）。当定义了这些“单元”时，人们承认物质和能量可以在相邻的“单元”之间自由地通过，其速度足以使“单元”（相对于强度变量）保持各自的局部热力学平衡。
One can think here of two 'relaxation times' separated by order of magnitude.<ref name="Zubarev 1971/1974">[[Dmitry Zubarev|Zubarev D. N.]],(1974). ''[https://books.google.com/books?id=SQy3AAAAIAAJ&hl=ru&source=gbs_ViewAPI Nonequilibrium Statistical Thermodynamics]'', translated from the Russian by P.J. Shepherd, New York, Consultants Bureau. {{ISBN|0-306-10895-X}}; {{ISBN|978-0-306-10895-2}}.</ref> The longer relaxation time is of the order of magnitude of times taken for the macroscopic dynamical structure of the system to change. The shorter is of the order of magnitude of times taken for a single 'cell' to reach local thermodynamic equilibrium. If these two relaxation times are not well separated, then the classical non-equilibrium thermodynamical concept of local thermodynamic equilibrium loses its meaning<ref name="Zubarev 1971/1974"/> and other approaches have to be proposed, see for instance [[Extended irreversible thermodynamics]]. For example, in the atmosphere, the speed of sound is much greater than the wind speed; this favours the idea of local thermodynamic equilibrium of matter for atmospheric heat transfer studies at altitudes below about 60 km where sound propagates, but not above 100 km, where, because of the paucity of intermolecular collisions, sound does not propagate.
One can think here of two 'relaxation times' separated by order of magnitude.<ref name="Zubarev 1971/1974">[[Dmitry Zubarev|Zubarev D. N.]],(1974). ''[https://books.google.com/books?id=SQy3AAAAIAAJ&hl=ru&source=gbs_ViewAPI Nonequilibrium Statistical Thermodynamics]'', translated from the Russian by P.J. Shepherd, New York, Consultants Bureau. {{ISBN|0-306-10895-X}}; {{ISBN|978-0-306-10895-2}}.</ref> The longer relaxation time is of the order of magnitude of times taken for the macroscopic dynamical structure of the system to change. The shorter is of the order of magnitude of times taken for a single 'cell' to reach local thermodynamic equilibrium. If these two relaxation times are not well separated, then the classical non-equilibrium thermodynamical concept of local thermodynamic equilibrium loses its meaning<ref name="Zubarev 1971/1974"/> and other approaches have to be proposed, see for instance [[Extended irreversible thermodynamics]]. For example, in the atmosphere, the speed of sound is much greater than the wind speed; this favours the idea of local thermodynamic equilibrium of matter for atmospheric heat transfer studies at altitudes below about 60 km where sound propagates, but not above 100 km, where, because of the paucity of intermolecular collisions, sound does not propagate.
在这里，人们可以想到两个“弛豫时间”之间的数量级分隔。较长的弛豫时间约为系统宏观动力学结构发生变化所需的时间量级。较短的是独立“单元”达到局部热力学平衡所需的时间量级。如果这两个驰豫时间没有很好地分开，那么局部热力学平衡的经典非平衡热力学概念就失去了意义，那么必须提出其他方法，例如扩展的不可逆热力学。例如，在大气中，音速远大于风速；这有利于物质的局部热力学平衡的想法，对于在低于60 km的高空进行大气传热研究，声音可以在其中传播，但需要限制在100 km以内，因为分子间碰撞发生的很少，因此声音无法传播。
=== Milne's definition in terms of radiative equilibrium 米尔恩Milne在辐射平衡系统方面的定义===
[[Edward Arthur Milne|Edward A. Milne]], thinking about stars, gave a definition of 'local thermodynamic equilibrium' in terms of the [[thermal radiation]] of the [[matter]] in each small local 'cell'.<ref name="Milne 1928">{{cite journal | last1= Milne |first1= E.A. |year=1928 | title= The effect of collisions on monochromatic radiative equilibrium |journal=[[Monthly Notices of the Royal Astronomical Society]] | volume= 88|issue= 6 |pages=493–502|bibcode=1928MNRAS..88..493M | doi = 10.1093/mnras/88.6.493 |doi-access= free }}</ref> He defined 'local thermodynamic equilibrium' in a 'cell' by requiring that it macroscopically absorb and spontaneously emit radiation as if it were in radiative equilibrium in a cavity at the [[temperature]] of the matter of the 'cell'. Then it strictly obeys Kirchhoff's law of equality of radiative emissivity and absorptivity, with a black body source function. The key to local thermodynamic equilibrium here is that the rate of collisions of ponderable matter particles such as molecules should far exceed the rates of creation and annihilation of photons.
[[Edward Arthur Milne|Edward A. Milne]], thinking about stars, gave a definition of 'local thermodynamic equilibrium' in terms of the [[thermal radiation]] of the [[matter]] in each small local 'cell'.<ref name="Milne 1928">{{cite journal | last1= Milne |first1= E.A. |year=1928 | title= The effect of collisions on monochromatic radiative equilibrium |journal=[[Monthly Notices of the Royal Astronomical Society]] | volume= 88|issue= 6 |pages=493–502|bibcode=1928MNRAS..88..493M | doi = 10.1093/mnras/88.6.493 |doi-access= free }}</ref> He defined 'local thermodynamic equilibrium' in a 'cell' by requiring that it macroscopically absorb and spontaneously emit radiation as if it were in radiative equilibrium in a cavity at the [[temperature]] of the matter of the 'cell'. Then it strictly obeys Kirchhoff's law of equality of radiative emissivity and absorptivity, with a black body source function. The key to local thermodynamic equilibrium here is that the rate of collisions of ponderable matter particles such as molecules should far exceed the rates of creation and annihilation of photons.
爱德华·米尔恩Edward A. Milne在研究恒星时，根据每个局部“小单元”中物质的热辐射来定义“局部热力学平衡”。他通过设定“吸收并自发辐射（宏观意义上）”这一基本要求，定义研究对象处在“细胞”物质温度的空腔中，类似辐射平衡状态一样。然后，它严格遵守关于辐射发射率和吸收率相等的基尔霍夫定律Kirchhoff's law，以及黑体源函数。这里达到局部热力学平衡的关键在于重要物质颗粒的碰撞速率，例如分子应远远超过光子的产生和湮灭的速率。
==Entropy in evolving systems==
==Entropy in evolving systems==