  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.
