Most modern memory modules are dynamic, which means that the memory must be constantly refreshed (re-energised) in order to retain its contents. This means that regardless of the amount of memory used, it will always be refreshed, which in term means that it will use a certain amount of power. Regardless of the content of a memory block it still needs to be refreshed.

http://stackoverflow.com/questions/12906083/correlation-between-memory-usage-of-processes-and-battery-consumption-android

https://superuser.com/questions/40113/does-installing-larger-ram-means-consuming-more-energy

https://www.quora.com/What-happens-to-your-energy-consumption-if-you-use-more-RAM

Chapter Evaluating the RAM Energy Consumption at the Stage of Softwa...

https://forums.anandtech.com/threads/ram-vs-energy.2355735/