Insights into the role of interactions in determining the macroscopic state of a system can be obtained by observing its evolution with an isothermal variation of density. We explore the isothermal evolution of the electron gas in AlOx/SrTiO3 by a continuous gate-controlled tuning of its carrier density across the phase diagram exhibiting a superconducting dome. It is seen that condensation of the ordered phase leads to non-monotonic isotherms within the superconducting dome. The system undergoes dynamic change lasting tens of seconds following changes in gate voltage near the onset of the transition, revealing a strong impact of structural defects and distortions of the substrate on the superconducting state. These observations suggest that AlOx/SrTiO3 is a promising platform to study time-dependent kinetic processes at the onset of superconductivity.
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