热电的可逆互易关系
Reversible Reciprocal Relation of Thermoelectricity
摘要：
第一开尔文关系式指出珀耳帖系数应该等于温度和塞贝克系数的乘积，这是热电学中的基本原理。它被认为是Onsager互反关系（ORR）的一个重要应用和直接的实验验证，是不可逆热力学的基石。然而，一些关键问题仍然存在：为什么Kelvin的证明，省略了所有的不可逆性在热电输运过程中可以得到正确的结果，如何正确地选择广义力通量对导出的第一个Kelvin关系ORR，以及第一个Kelvin关系是否受到限制的线性输运制度的要求。本文的工作就是基于热力学基本原理来回答这些问题。由于热电效应是可逆的，我们可以重新定义的塞贝克和珀尔帖系数的数量在可逆过程中没有涉及的时间导数，这被重新命名为“可逆塞贝克和珀尔帖系数”。它们之间的关系（称为“可逆的热电互逆关系”）是从麦克斯韦关系导出的，当采用局部平衡假设（LEA）时，麦克斯韦关系可以简化为传统的开尔文关系。在这个意义上，第一开尔文关系的有效性是由可逆热力学原理和LEA保证的，而不需要线性输运过程。此外，从ORR获得第一开尔文关系的广义力-通量对在数学上和数学上都是正确的，只有当它们对应于麦克斯韦关系可以产生可逆互逆关系的共轭变量对时。本理论框架可以进一步扩展到其他耦合现象。
英文摘要：
The first Kelvin relation that states the Peltier coefficient should be equal to the product of temperature and Seebeck coefficient is a fundamental principle in thermoelectricity. It has been regarded as an important application and direct experimental verification of Onsager reciprocal relation (ORR) that is a cornerstone of irreversible thermodynamics. However, some critical questions still remain: why Kelvin's proof that omits all irreversibility within a thermoelectric transport process can reach the correct result, how to properly select the generalized-force-flux pairs for deriving the first Kelvin relation from ORR, and whether the first Kelvin relation is restricted by the requirement of linear transport regime. The present work is to answer these questions based on the fundamental thermodynamic principles. Since the thermoelectric effects are reversible, we can redefine the Seebeck and Peltier coefficients using the quantities in reversible processes with no time derivative involved, which are renamed as "reversible Seebeck and Peltier coefficients". The relation between them (called "the reversible reciprocal relation of thermoelectricity") is derived from the Maxwell relations, which can be reduced to the conventional Kelvin relation, when the local equilibrium assumption (LEA) is adopted. In this sense, the validity of the first Kelvin relation is guaranteed by the reversible thermodynamic principles and LEA, without the requirement of linear transport process. Additionally, the generalized force-flux pairs to obtain the first Kelvin relation from ORR can be proper both mathematically and thermodynamically, only when they correspond to the conjugate-variable pairs of which Maxwell relations can yield the reversible reciprocal relation. The present theoretical framework can be further extended to other coupled phenomena.
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