  We report the discovery of hysteresis between the x-ray spectrum and
luminosity of black-hole binary LMC X-3. Our observations, with the
Proportional Counter Array on the Rossi X-ray Timing Explorer, took place
entirely within the soft spectral state, dominated by a spectral component that
was fitted well with a multicolor disk blackbody. A power-law component was
seen only during times when the luminosity of the disk blackbody was declining.
The x-ray luminosity at these times was comparable to that seen in transient
systems (x-ray novae) when they return to the hard state at the end of an
outburst. Our observations may represent partial transitions to the hard state;
complete transitions have been seen in this system by Wilms et al. (2001). If
they are related to the soft-to-hard transition in transients, then they
demonstrate that hysteresis effects can appear without a full state transition.
We discuss these observations in the context of earlier observations of
hysteresis within the hard state of binaries 1E 1740.7-2942 and GRS 1758-258
and in relation to published explanations of hysteresis in transients.
