We investigate the impact of transport current on the superconducting order parameter in superconducting islands in full-shell epitaxial Al-InAs nanowires. Depending on the device layout, the suppression of superconductivity occurs in three fundamentally different ways-by a critical current in the case of superconducting reservoirs and by a critical voltage or by a critical Joule power in the case of normal reservoirs. In the latter case, the collapse of the superconducting state depends on the ratio of the dwell time and the electron-phonon relaxation time of quasiparticles in the island. For low resistive and high resistive coupling to the reservoirs, respectively, a relaxation-free regime and a strong electron-phonon relaxation regime are realized. Our results shed light on the potential shortcomings of finite-bias transport spectroscopy in floating islands.

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• Electron relaxation
• Electron-phonon coupling
• Proximity effect
• Superconducting order parameter
• Nanowires
• Superconductivity
• Usadel equation