In this talk, I will discuss two peculiar but important examples of how spacetime geometry and statistical fluctuations interact with quantumness. I will first discuss the interplay of topology and boundary conditions with quantum entanglement. In particular, I will show how a simple entanglement monotone related to geometric entanglement is a bona fide and experimentally measurable quantifier of topological order in many-body quantum systems. I will then discuss the relevance of time ordering between active quantum operations and thermal noise. In particular, I will show that active squeezing of initially thermal states, leading to so-called squeezed thermal states, yields a degree of quantum discord and quantum coherence that, at fixed squeezing, increase with the amount of noise originally present in the thermal input. One can then convert the increased coherence into increased entanglement by standard procedures.