Supercooled liquids exhibit a pronounced slowdown of their dynamics on cooling¹ without showing any obvious structural or thermodynamic changes². Several theories relate this slowdown to increasing spatial correlations^{3, 4, 5, 6}. However, no sign of this is seen in standard static correlation functions, despite indirect evidence from considering specific heat⁷ and linear dielectric susceptibility⁸. 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.

1. CEA, DSM, Institut de Physique Théorique, IPhT, CNRS, MPPU, URA2306, Saclay, F-91191 Gif-sur-Yvette, France
2. Science & Finance, Capital Fund Management, 6 Bd Haussmann, 75009 Paris, France
3. Centre for Statistical Mechanics and Complexity (SMC), CNR-INFM, Via dei Taurini 19, 00185 Roma, Italy
4. Instituto de Investigaciones Fisicoquímicas Teóricas y Aplicadas (INIFTA– CCT La Plata) and Departamento de Física, Facultad de Ciencias Exactas, Universidad Nacional de La Plata, c.c. 16, suc. 4, 1900 La Plata, Argentina
5. Consejo Nacional de Investigaciones Científicas y Técnicas, c.c. 16, suc. 4, 1900 La Plata, Argentina
6. Dipartimento di Fisica, Università di Trento, via Sommarive 14, 38050 Povo, Trento, Italy

Correspondence to: T. S. Grigera^4,5 e-mail: tgrigera@inifta.unlp.edu.ar