Electrical Current Generation by Sorting Thermal Noise
We have achieved the operation of Maxwell’s demon with an electrical device, which is a feedback operation based on single-electron motion. Maxwell’s demon is related to the lower bound of energy consumption in electrical devices and power generation efficiency in small systems. We therefore anticipate that this achievement will contribute to creating nanoscale energy-efficient electrical devices.
Keywords: thermal noise, silicon transistor, Maxwell’s demon
1. Second law of thermodynamics and Maxwell’s demon
The second law of thermodynamics states that every physical system eventually becomes random. This law prohibits us from creating ordered motion of electrons, or electrical current, from thermal noise unless we modify the electrons externally. Maxwell’s demon is a thought experiment created by Scottish mathematician James Clerk Maxwell to contradict the second law of thermodynamics; it is an ideal entity that can perform a feedback operation by observing objects at the level of thermal noise and can create ordered motion of electrons using energy from thermal noise without our having to modify the electrons.
Maxwell’s demon has been vigorously discussed among physicists for more than 150 years because it appears to violate the second law. The discussions have clarified that Maxwell’s demon uses information about the thermal motion of electrons, which requires energy. This means that we need a certain amount of energy to obtain the information, and we can create the same amount of energy at maximum from it.
This idea leads to the concept of information thermodynamics, in which the role of information is on the same footing as energy. Information thermodynamics reveals the lower bounds of the thermodynamic cost of information processing  and provides us knowledge about small heat engines such as molecular motors whose motions are driven by thermal fluctuations. Maxwell’s demon is the epitome of information thermodynamics, which is considered to be related to energy-efficient biological systems.
In this study, we succeeded in generating electrical current and power with Maxwell’s demon in one of the most natural ways: observing electron thermal motion, sorting electrons with the obtained information, and outputting the sorted electrons that had large energy.
2. Silicon nanotransistors and operation of Maxwell’s demon
In the experiment, we used a silicon nanodevice on a silicon-on-insulator wafer. In our device, a single-electron box electrostatically defined by two transistors provides doors through which electrons can enter and exit the box, and a capacitively coupled detector with single-electron sensitivity detects thermal fluctuation in the box at the single-electron level (Fig. 1) . By switching the transistors on and off, we can open and close the entrance to the box and the exit from it individually. The number of electrons in the box was observed in real time at a frequency of about 14 Hz by measuring the current flowing through the detector. All the measurements were done at room temperature.
We performed feedback control based on the number of electrons in the box  as follows (Fig. 2). First, we open the entrance and observe random electron motion between the entrance and the box. After electrons have entered the box, we close the entrance. Then, we open the exit and observe random electron motion between the exit and the box. Finally, after the electrons have exited the box, the exit is closed. By repeating these procedures, we can move electrons from the entrance to the exit. We carefully calibrated the experimental setup to achieve the operation of Maxwell’s demon without doing any external work on the electrons .
3. Rectification of thermal noise with Maxwell’s demon
Carrying out the above procedures enables sorted electrons to flow as electrical current. They can even climb up the potential energy across the entrance and exit (Fig. 3); this climbing is the power generation. When the source-drain bias voltage VSD is ~30 mV, the generated power shows the maximum value of 0.5 zW (10−21 W). The quantitatively estimated information-to-energy conversion efficiency is 18%, which is reasonably high and consistent with our theoretical simulation. This consistency indicates that silicon nanodevices are an ideal platform for studying Maxwell’s demon and information thermodynamics. The simulation also demonstrated that the power output increases as the detector becomes faster and the box becomes smaller. Therefore, further advances in transistor technology will lead to an increase in the demon’s power output.
4. Future work
The results in this work are closely related to the lower bound of energy consumption in electrical devices and the efficiency of small heat engines. To achieve high energy-to-power conversion efficiency, biomolecules, for example, molecular motors, are thought to use information about themselves to perform their operation at proper timings. Such an efficient process in biomolecules can be modeled and analyzed in the framework of Maxwell’s demon. We will attempt in the future to deepen our understanding of the mechanism responsible for the high efficiency in biological systems and thereby make an electrical device that mimics their high efficiency.