In fluids under temperature gradients, long-range correlations (LRCs) emerge generically, leading to enhanced density fluctuations. This phenomenon, characterized by the ${\mathit{q}}^{-4}$ divergence in the static structure factor (where $\mathit{q}$ is the wavenumber), has been extensively studied both theoretically and experimentally. However, they remain unexplored in Hamiltonian particle systems using molecular dynamics (MD) simulations. This Letter reports the first MD study to provide unambiguous observations of the LRCs. We demonstrate this by three distinct approaches: (i) measuring the static structure factor and directly observing the ${\mathit{q}}^{-4}$ divergence characterizing the LRCs; (ii) detecting the corresponding ${\mathit{q}}^{-4}$ divergence in the dynamic structure factor; and (iii) establishing a quantitative agreement between MD results and predictions from fluctuating hydrodynamics, the phenomenological theory that predicts the LRCs. Our findings demonstrate that MD simulations offer a powerful complementary tool to theoretical and experimental investigations of LRCs.

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• Fluctuations & noise
• Nonequilibrium statistical mechanics
• Molecular dynamics
• Stochastic differential equations