Many neuromorphic computing architectures contain emerging memory devices that function through oxygen migration. Examples include resistive memory1 (ReRAM) and electrochemical memory2 (ECRAM), where tuning the distribution of oxygen vacancies enables analog information states. In this presentation, we discuss how oxygen transport in many metal oxides do not obey the drift-diffusion equation, which assumes ideal solution thermodynamics. Instead, the metal oxides undergo composition phase separation into oxygen-rich and oxygen-poor phases. This phase separation explains the long information retention time of ReRAM3. We further use this phase separation to improve the information retention time of oxygen-based ECRAM4,5 by at least ten orders of magnitude, yielding the highest temperature analog nonvolatile memory.