“耗散”的版本间的差异

2021年1月31日 (日) 22:29的版本

在热力学中,耗散 dissipation是在均匀热力学系统中发生的不可逆过程。耗散过程是能量(内能、整体流动动力学或系统势能)从某种初态转化为某种终态的过程，终态做机械功的能力小于初态做机械功的能力。例如，热传递是耗散的，因为它是内能从一个较热的物体向一个较冷的物体的转移。根据热力学第二定律，熵随温度变化(降低了两个物体组合做机械功的能力) ，但是在一个孤立的系统中熵从不减少。

这些过程以一定的速率产生熵（熵产生 entropy production)。熵产生速率乘以环境温度就得到了耗散功率。不可逆过程的重要例子有: 热流 heat flow通过热阻 thermal resistance，流体 fluid flow流过流阻，扩散(混合) ，化学反应 chemical reactions，电流 electric current流过电阻 electrical resistance(焦耳加热 joule heating)。

定义

热力学耗散过程本质上是不可逆的。它们以有限的速率产生熵。在一个局部连续定义温度的过程中，熵产生速率的局部密度乘以局部温度得到局部耗散功率密度。

耗散过程的一个特殊现象不能用一个单独的哈密顿 Hamiltonian形式来描述。耗散过程需要一组可容许的个体哈密顿量描述，确切地说，描述感兴趣的过程的实际特殊现象是未知的。这包括摩擦力和所有导致能量消相干的类似力，即将相干性 coherent或定向能量流转换为非定向或更各相同性 isotropic的能量分布。

能量

“机械能转化为热能的过程叫做能量耗散”——弗朗索瓦·罗迪 François Roddier^[1]，这一术语也用于指电力和电子电路中由于产生不必要的热量而造成的能量损失。

计算物理学 Computational physics

在计算物理学 computational physics中，数值耗散（也称为“数值扩散”）是指微分方程数值解可能产生的某些副作用。当用数值近似方法求解无耗散的纯平流 advection方程时，初始波的能量可以用类似于扩散过程的方式降低。这种方法被称为包含“耗散”。在某些情况下，故意添加“人工耗散”来改善解的数值稳定性 numerical stability特性。^[2]

数学 Mathematics

漫游集 wandering sey文章中给出了在保测度动力系统 measure-preserving dynamical system的数学研究中常用的耗散的形式化数学定义。

例子

在水利工程中 In hydraulic engineering

耗散是将向下流动的水的机械能转化为热能和声能的过程。在河床上设计了各种装置，以降低水流的动能，减少它们对河岸和河底的 侵蚀潜力 erosive potential。很多时候，这些装置看起来像小瀑布或瀑布，水流垂直流动或越过抛石失去一些 动能 kinetic energy。

不可逆过程 Irreversible processes

不可逆过程的重要例子有:

热流通过热阻
流体流过流阻
扩散(混合)
化学反应^[3]^[4]
电流通过电阻(焦耳加热)。

波或振荡 Waves or oscillations

波或振荡，通常会由于摩擦或紊流而随着时间的推移失去能量。在许多情况下，“损失”的能量提高了系统的温度。例如，失去振幅的波叫做消散波。影响的确切性质取决于波的性质: 例如，大气波可能由于与地块的摩擦而于接近地表处消散，由于辐射冷却的缘故而在更高的水平上消散。

历史

耗散的概念是由威廉·汤姆森 William Thomson于1852年引入热力学领域的。^[5]William推断，上述不可逆耗散过程的一个子集将会发生，除非一个过程由一个“完美的热机”控制。开尔文勋爵确定的过程是摩擦、扩散、热传导和光吸收。

参见

熵产生 Entropy production

防洪 Flood control

最大熵准则 Principle of maximum entropy

二维气体 Two-dimensional gas

参考文献

↑ Roddier F., Thermodynamique de l'évolution (The Thermodynamics of Evolution), parole éditions, 2012
↑ Thomas, J.W. Numerical Partial Differential Equation: Finite Difference Methods. Springer-Verlag. New York. (1995)

↑ Glansdorff, P., Prigogine, I. (1971). Thermodynamic Theory of Structure, Stability, and Fluctuations, Wiley-Interscience, London, 1971,

, p. 61.

↑ Eu, B.C. (1998). Nonequilibrium Thermodynamics: Ensemble Method, Kluwer Academic Publications, Dordrecht,

, p. 49,

↑ W. Thomson On the universal tendency in nature to the dissipation of mechanical energy Philosophical Magazine, Ser. 4, p. 304 (1852).

本中文词条由Henry审校，Bai审校，薄荷欢迎在讨论页面留言。

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[1] Roddier F., Thermodynamique de l'évolution (The Thermodynamics of Evolution), parole éditions, 2012

[2] Thomas, J.W. Numerical Partial Differential Equation: Finite Difference Methods. Springer-Verlag. New York. (1995)

[3] Glansdorff, P., Prigogine, I. (1971). Thermodynamic Theory of Structure, Stability, and Fluctuations, Wiley-Interscience, London, 1971,
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[4] Eu, B.C. (1998). Nonequilibrium Thermodynamics: Ensemble Method, Kluwer Academic Publications, Dordrecht,
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[5] W. Thomson On the universal tendency in nature to the dissipation of mechanical energy Philosophical Magazine, Ser. 4, p. 304 (1852).

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