  We prove that for any Monte Carlo algorithm of Metropolis type, the
autocorrelation time of a suitable ``energy''-like observable is bounded below
by a multiple of the corresponding ``specific heat''. This bound does not
depend on whether the proposed moves are local or non-local; it depends only on
the distance between the desired probability distribution $\pi$ and the
probability distribution $\pi^{(0)}$ for which the proposal matrix satisfies
detailed balance. We show, with several examples, that this result is
particularly powerful when applied to non-local algorithms.
