  The grand potential $\Omega$ and the response $R = - \partial \Omega
/\partial x$ of a phase-coherent confined noninteracting electron gas depend
sensitively on chemical potential $\mu$ or external parameter $x$. We compute
their autocorrelation as a function of $\mu$, $x$ and temperature. The result
is related to the short-time dynamics of the corresponding classical system,
implying in general the absence of a universal regime. Chaotic, diffusive and
integrable motions are investigated, and illustrated numerically. The
autocorrelation of the persistent current of a disordered mesoscopic ring is
also computed.
