Thermodynamic signature of growing amorphous order in glass-forming liquids

Supercooled liquids exhibit a pronounced slowdown of their dynamics on cooling(1) without showing any obvious structural or thermodynamic changes(2). Several theories relate this slowdown to increasing spatial correlations(3-6). However, no sign of this is seen in standard static correlation functions, despite indirect evidence from considering specific heat(7) and linear dielectric susceptibility(8). Whereas the dynamic correlation function progressively becomes more non-exponential as the temperature is reduced, so far no similar signature has been found in static correlations that can distinguish qualitatively between a high-temperature and a deeply supercooled glass-forming liquid in equilibrium. Here, we show evidence of a qualitative thermodynamic signature that differentiates between the two. We show by numerical simulations with fixed boundary conditions that the influence of the boundary propagates into the bulk over increasing length scales on cooling. With the increase of this static correlation length, the influence of the boundary decays non-exponentially. Such long-range susceptibility to boundary conditions is expected within the random first-order theory(4,9,10) (RFOT) of the glass transition. However, a quantitative account of our numerical results requires a generalization of RFOT, taking into account surface tension fluctuations between states.