Shuster, J. R.Gershman, D. J.Giles, B. L.Bessho, N.Sharma, A. S.Dorelli, J. C.Uritsky, V.Schwartz, S. J.Cassak, P. A.Denton, R. E.Chen, L.-J.Gurram, H.Ng, J.Burch, J.Webster, J.Torbert, R.Paterson, W. R.Schiff, C.Viñas, A. F.Avanov, L. A.Stawarz, J.Li, T. C.Liu, Y.-H.Argall, M. R.Afshari, A.Payne, D. S.Farrugia, C.J.Verniero, J.Wilder, F.Genestreti, K.da Silva, D. E.Temporal, spatial, and velocity-space variations of electron phase space density are measured observationally and compared for the first time using the four magnetospheric multiscale (MMS) spacecraft at Earth's magnetopause. Equipped with these unprecedented spatiotemporal measurements offered by the MMS tetrahedron, we compute each term of the electron Vlasov equation that governs the evolution of collisionless plasmas found throughout the universe. We demonstrate how to use single spacecraft measurements to improve the resolution of the electron pressure gradient that supports nonideal parallel electric fields, and we develop a model to intuit the types of kinetic velocity-space signatures that are observed in the Vlasov equation terms. Furthermore, we discuss how the gradient in velocity-space sheds light on plasma energy conversion mechanisms and wave-particle interactions that occur in fundamental physical processes such as magnetic reconnection and turbulence.en-USmagnetic reconnectionmagnetopauseVlasov equationkinetic theorydistribution functioncollisionless plasmaArticle