# Thermodynamic inconsistency of the conventional theory of superconductivity

## TL;DR

The paper demonstrates that the conventional theory of superconductivity predicts thermodynamic inconsistencies during temperature changes in type I superconductors, challenging its validity and suggesting an alternative theory may be necessary.

## Contribution

It identifies a fundamental thermodynamic inconsistency in the conventional theory of superconductivity during temperature variation processes.

## Key findings

- Conventional theory predicts Joule heat generation dependent on temperature change rate.
- The process violates the first and second laws of thermodynamics under conventional assumptions.
- An alternative theory of hole superconductivity may resolve these issues.

## Abstract

A type I superconductor expels a magnetic field from its interior to a surface layer of thickness $\lambda_L$, the London penetration depth. $\lambda_L$ 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.