On the Clausius-Duhem Inequality and Maximum Entropy Production in a Simple Radiating System
On the Clausius-Duhem Inequality and Maximum Entropy Production in a Simple Radiating System
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简单辐射系统中的克劳修斯-迪昂不等式和最大熵产生
DOI：
10.3390/e16042291
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发表时间：
2014
期刊：
影响因子：
2.7
通讯作者：
J. Pelkowski
中科院分区：
文献类型：
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作者：
J. Pelkowski
一颗被太阳照射的黑色行星作为一个简单的辐射双层系统的原型，在稳定的日照下允许连续的稳定状态。稳定的熵产生率可以计算出某一层的不同不透明度，明确地计算出辐射相互作用，间接地计算出维持每一层热均匀性所涉及的所有物质的不可逆性。热力学第二定律有两个版本，一个是著名的克劳修斯-迪昂不等式，另一个是现代版本的熵不等式。通过最大化物质熵产生率，可以选择一个总是满足克劳修斯-迪昂不等式的状态。一些形式上可能的稳态，虽然违反后者，但仍然服从熵不等式。就地球气候而言，任何“温室效应”都显示出全球熵产率的极值。然而，只有当模型被接受为地球气候的代表时，才会发现极端值与观测到的大气和地表的（有效）温度不一致。尽管如此，目前地球上温室效应的总熵产率非常接近地球有效温度下均匀变暖稳定状态的最大熵产率。对于温室效应较弱的地球来说，这种说法不再成立。
A black planet irradiated by a sun serves as the archetype for a simple radiating two-layer system admitting of a continuum of steady states under steadfast insolation. Steady entropy production rates may be calculated for different opacities of one of the layers, explicitly so for the radiative interactions, and indirectly for all the material irreversibilities involved in maintaining thermal uniformity in each layer. The second law of thermodynamics is laid down in two versions, one of which is the well-known Clausius-Duhem inequality, the other being a modern version known as the entropy inequality. By maximizing the material entropy production rate, a state may be selected that always fulfills the Clausius-Duhem inequality. Some formally possible steady states, while violating the latter, still obey the entropy inequality. In terms of Earth’s climate, global entropy production rates exhibit extrema for any “greenhouse effect”. However, and only insofar as the model be accepted as representative of Earth’s climate, the extrema will not be found to agree with observed (effective) temperatures assignable to both the atmosphere and surface. This notwithstanding, the overall entropy production for the present greenhouse effect on Earth is very close to the maximum entropy production rate of a uniformly warm steady state at the planet’s effective temperature. For an Earth with a weak(er) greenhouse effect the statement is no longer true.