A type I superconductor expels a magnetic field from its interior to a surface layer of thickness [Formula: see text], the London penetration depth. [Formula: see text] is a function of temperature, becoming smaller as the temperature decreases. Here we analyze the process of cooling (or heating) a type I superconductor in a magnetic field, with the system remaining always in the superconducting state. The conventional theory predicts that Joule heat is generated in this process, the amount of which depends on the rate at which the temperature changes. Assuming the final state of the superconductor is independent of history, as the conventional theory assumes, we show that this process violates the first and second laws of thermodynamics. We conclude that the conventional theory of superconductivity is internally inconsistent. Instead, we suggest that the alternative theory of hole superconductivity may be able to resolve this problem.

中文翻译：

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传统超导理论的热力学不一致

I 型超导体将磁场从其内部排出到厚度为 [公式：见正文] 的表面层，即伦敦穿透深度。【公式：见正文】是温度的函数，随温度降低而变小。在这里，我们分析了在磁场中冷却（或加热）I 型超导体的过程，系统始终处于超导状态。传统理论预测，在这个过程中会产生焦耳热，其数量取决于温度变化的速率。假设超导体的最终状态与历史无关，正如传统理论所假设的那样，我们证明这个过程违反了热力学第一和第二定律。我们得出结论，传统的超导理论在内部是不一致的。反而，