Temporal velocity correlations of diffusing particles carry information about the structure of the diffusion environment. Studying high-order velocity autocorrelation functions can aid in understanding how signal is influenced by restricted diffusion and exchange, and in turn how to design experiments that are sensitive/independent to these phenomena. In this work, we employ numerical simulations on a variety of substrates to demonstrate this notion. We find that the fourth order velocity autocorrelation bears a distinctive signature of exchanging systems. In addition, we highlight that the effect of exchange on the second order velocity autocorrelation is negligible when exchange is barrier-limited.
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