论文标题
热力学第二定律在连续物理学中的作用：重新审视muschik和ehrentrentraut定理
The Role of Second Law of Thermodynamics in Continuum Physics: A Muschik and Ehrentraut Theorem Revisited
论文作者
论文摘要
热力学的第二定律强调，在任何热力学过程中，熵产生必须无负。在连续物理学中，通过假定代表体材料特性的本构方程以一种方式，以使第二种热力学定律在任意过程中满足体系的材料特性，从而满足了这种要求。这种方法最初是在Coleman和Noll \ cite {Colnol}以及Coleman和Mizel和Mizel \ cite {Colmiz}的一些开创性论文中，实际上将热力学定律视为对本构方程的限制，必须保证任何解决平衡法律的解决方案也可以满足熵的任何解决方案。正如Muschik和Ehrentraut \ Cite {Musehr}所观察到的那样，这是一个有用的操作假设，但不是一般物理定律的结果。实际上，将热力学第二定律视为对热力学过程的限制，即对平衡法则的解决方案的限制。这是因为存在满足熵不平等的平衡法的解决方案，而解决方案则无法满足。为了确定正确的方法是什么，Muschik和Erhentraut假定了第二定律的修正案，这使得明显但隐藏的假设是，在身体的任何点中，熵产生为零，并且只有此点才是热力学平衡。然后，他们证明，鉴于修正案，热力学的第二定律必然是对本构方程而不是热力学过程的限制。在本文中，我们重新审视了它们的证明，点燃了一些隐藏在参考文献中的几何方面。 \ cite {musehr}。此外，我们提出了一种融合了修正案的热力学第二定律的替代制定。
Second law of thermodynamics imposes that in any thermodynamic process the entropy production must be nonnegative. In continuum physics such a requirement is fulfilled by postulating the constitutive equations which represent the material properties of the bodies in such a way that second law of thermodynamics is satisfied in arbitrary processes. Such an approach, first assumed in some pioneering papers by Coleman and Noll \cite{ColNol} and Coleman and Mizel \cite{ColMiz}, in practice regards second law of thermodynamics as a restriction on the constitutive equations, which must guarantee that any solution of the balance laws satisfies also the entropy inequality. As observed by Muschik and Ehrentraut \cite{MusEhr}, this is a useful operative assumption, but not a consequence of general physical laws. Indeed, a different point of view, which regards second law of thermodynamics as a restriction on the thermodynamic processes, i.e., on the solutions of the system of balance laws, is possible. This is tantamount to assume that there are solutions of the balance laws which satisfy the entropy inequality, and solutions which do not satisfy it. In order to decide what is the correct approach, Muschik and Erhentraut postulated an amendment to the second law, which makes explicit the evident but rather hidden assumption that in any point of the body the entropy production is zero if, and only if, this point is thermodynamic equilibrium. Then they proved that, given the amendment, second law of thermodynamics is necessarily a restriction on the constitutive equations and not on the thermodynamic processes. In the present paper we revisit their proof, lighting up some geometric aspects which were hidden in Ref. \cite{MusEhr}. Moreover, we propose an alternative formulation of second law of thermodynamics which incorporates the amendment.
