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
It's more like a generator that uses ambient heat as the "battery". With previous systems you could only extract useful work from heat if you had a heat gradient (e.g. one area that's hotter than another). With this invention the innovation is that graphene's unique combination of thinness and conductivity basically let you convert the brownian "heat" of the substance itself (not the environment) into electricity.
I couldnt access the full text, but that was my impression, too, based on the summary. It appears to work on some analog of hysteresis where the technical balance of energy is maintained but the time scale of restitution is long enough that power can be "siphoned off". Again - since conservation of energy must be preserved and no matter is created or destroyed, this would serve to reduce the temperature of the graphene. There doesn't appear to be a scale for their experimental work and whether they're extracting pico amps or microamps across the (I guessing form the publicly available graphs) 0-0.4 volt potential.
It's not clear if they're looking at nominally uniform temperature material which has fluctuations in temperature due to the surroundings, or if they are inducing temperature gradients in the material intentionally to produce the signal. I'm an engineer, not a theoretical physicist, so anyone claiming to end-run the second law of thermodynamics is going to be treated with a bit of skepticism as to the practicality or scalability of this "cheat".
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 :)
A law is only effective if the majority is following it. But we will never escape this system if we follow the rules of the system itself. I'm calling for scientists to finally just break the laws of thermodynamics!