  We propose and numerically implement a local probe of the static self-induced
heterogeneity characterizing glass-forming liquids. The method relies on the
equilibrium statistics of the overlap between pairs of configurations measured
in mesoscopic cavities with unconstrained boundaries. By systematically
changing the location of the probed cavity, we directly detect spatial
variations of the overlap fluctuations. We provide a detailed analysis of the
statistics of a local estimate of the configurational entropy and we infer an
estimate of the surface tension between amorphous states, ingredients that are
both at the basis of the random first-order transition theory of glass
formation. Our results represent the first direct attempt to visualize and
quantify the self-induced heterogeneity underpinning the thermodynamics of
glass formation. They pave the way for the development of coarse-grained
effective theories and for a direct assessment of the role of thermodynamics in
the activated dynamics of deeply supercooled liquids.
