Scientists have figured out how to harness Brownian motion – literally the thermal energy of individual molecules – to make electricity, by cleverly connecting diodes up to pieces of graphene, which are atom-thick sheets of Carbon. The team has successfully demonstrated their theory (which was previously thought to be impossible by prominent physicists like Richard Feynman), and are now trying to make a kind of micro-harvester that can basically produce inexhaustible power for things like smart sensors.
The most impressive thing about the system is that it doesn’t require a thermal gradient to do work, like other kinds of heat-harvesting systems (Stirling engines, Peltier junctions, etc.). As long as it’s a bit above absolute zero, there’s enough thermal energy “in the system” to make the graphene vibrate continuously, which induces a current that the diodes can then pump out.
Original journal link: https://journals.aps.org/pre/abstract/10.1103/PhysRevE.108.024130
I think this is it exactly, and in fact I found a Science Daily article that explains the cleverness of it (your assumption about the time scale is correct, and they have a clever arrangement of diodes that let you kind of “pump” the charge out). They specifically mention not violating the 2nd Law too :)