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We study theoretically and numerically a family of multi-point dynamicsusceptibilities that quantify the strength and characteristic lengthscales ofdynamic heterogeneities in glass-forming materials. We use general theoreticalarguments (fluctuation-dissipation relations and symmetries of relevantdynamical field theories) to relate the sensitivity of averaged two-timecorrelators to temperature and density to spontaneous fluctuations of the localdynamics. Our theoretical results are then compared to molecular dynamicssimulations of the Newtonian, Brownian and Monte-Carlo dynamics of tworepresentative glass-forming liquids, a fragile binary Lennard-Jones mixtureand a model for the strong glass-former silica. We justify in detail the claimmade in [Science 310, 1797 (2005)], that the temperature dependence ofcorrelation functions allows one to extract useful information on dynamiclengthscales in glassy systems. We also discuss some subtle issues associatedto the choice of microscopic dynamics and of statistical ensemble throughconserved quantities, which are found to play an important role in determiningdynamic correlations.Comment: 24 pages, 7 figs - Several discussions added (Arrhenius systems,  hydrodynamic contributions, relation between susceptibilities and  lengthscales, etc.

Spontaneous and induced dynamic fluctuations in glass formers. I. General results and dependence on ensemble and dynamics