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Jamming is a geometric phase transition occurring in dense particle systemsin the absence of temperature. We use computer simulations to analyse theeffect of thermal fluctuations on several signatures of the transition. We showthat scaling laws for bulk and shear moduli only become relevant when thermalfluctuations are extremely small, and propose their relative ratio as aquantitative signature of jamming criticality. Despite the nonequilibriumnature of the transition, we find that thermally induced fluctuations andmechanical responses obey equilibrium fluctuation-dissipation relations nearjamming, provided the appropriate fluctuating component of the particledisplacements is analysed. This shows that mechanical moduli can be directlymeasured from particle positions in mechanically unperturbed packings, andsuggests that the definition of a "nonequilibrium index" is unnecessary foramorphous materials. We find that fluctuations of particle displacements arespatially correlated, and define a transverse and a longitudinal correlationlengthscales which both diverge as the jamming transition is approached. Weanalyse the frozen component of density fluctuations and find that it displayssignatures of nearly-hyperuniform behaviour at large lengthscales. Thisdemonstrates that hyperuniformity in jammed packings is unrelated to avanishing compressibility and explains why it appears remarkably robust againsttemperature and density variations. Differently from jamming criticality,obstacles preventing the observation of hyperuniformity in colloidal systems donot originate from thermal fluctuations.

Thermal fluctuations, mechanical response, and hyperuniformity in jammed solids