We present an in silico study of the neuromorphic-computing behavior of the prototypical phase-change material, Ge2Sb2Te5, using ab initio molecular-dynamics simulations. Stepwise changes in structural order in response to temperature pulses of varying length and duration are observed, and a good reproduction of the spike-timing-dependent plasticity observed in nanoelectronic synapses is demonstrated. Short above-melting pulses lead to instantaneous loss of structural and chemical order, followed by delayed partial recovery upon structural relaxation. We also investigate the link between structural order and electrical and optical properties. These results pave the way toward a first-principles understanding of phase-change physics beyond binary switching.