Takahiro SAGAWA, Kyoto University
The unification of thermodynamics and information theory has been one of the most fundamental topics in physics, which is related to the foundation of the second law of thermodynamics . This topic dates back more than a century. In 1867, James C. Maxwell, a distinguished physicist in the nineteenth century, proposed a paradoxical concept that has been referred to as “Maxwell’s demon.” In his gedankenexperiment, the demon has the capability to access the microscopic degrees of freedom of a thermodynamic system. For example, the demon can observe the velocities of individual molecules at the level of thermal fluctuations. The demon then controls the thermodynamic system by using the obtained information about the microscopic world (i.e., the control protocol depends on the obtained outcomes), which is regarded as feedback control. By doing so, the demon can extract a positive amount of work from a thermodynamic cycle. Then, the role of the demon seems to be a sharp contradiction to the second law of thermodynamics. Here, the second law states that any positive amount of work cannot be extracted from a single heat bath by a thermodynamic cycle, or equivalently, a perpetual motion of the second kind is impossible. Since then, numerous arguments have been conducted on the paradox of Maxwell’s demon by physicists and philosophers. Does the demon really contradict to the second law? If not, what saves the second law from the demon?
2. Modern Perspective
Due to the advancements in the theories of statistical physics and information science, it is now understood that the demon is indeed consistent with the second law if we take into account the role of information in thermodynamics. Moreover, it has been recognized that the demon plays the key role to construct a unified theory of information and thermodynamics. From the modern point of view, the demon is regarded as a feedback controller that can use the obtained information as a resource of the work or the free energy. Such an engine controlled by the demon can be called an information heat engine.
3. Our Experiment and Theory
In 2010, our group has experimentally realized an information heat engine for the first time . We prepared a colloidal particle of the submicron scale, which behaves as a Brownian particle. We then measured the position of the particle, and performed feedback control by using electrodes. We succeeded to increase the free energy of the particle than the input work, which implies that the obtained information was successfully converted to the free energy. The conversion rate from information to the free energy was 28% in our experiment.
Moreover, we have constructed a general theory of thermodynamics of information processing on the basis of statistical physics and information theory [3-5]. We have derived a generalized second law of thermodynamics that involves information contents such as the Shannon information and the mutual information. The generalized second law reveals the fundamental limit of the energy cost that is needed for information processing such as measurement, information erasure, and feedback control.
4. Generalized Fluctuation Theorem
The conventional second law of thermodynamics is expressed in terms of an inequality. In contrast, the second law can be expressed in terms of equalities if we take into account the fluctuations of thermodynamic quantities. A prominent example of such equalities was found in 1990’s and has been called the fluctuation theorem. We have theoretically derived a generalized fluctuation theorem that includes the effect of feedback control, and experimentally verified it by using the aforementioned system.
The topic of this talk is the recent advancements on the relationship between thermodynamics and information, which is illuminated by a longstanding paradox of Maxwell’s demon. Our experiment validates that the demon can exist in the real world beyond the gedankenexperiment. Moreover, we have derived the second law of “information thermodynamics,” in which information contents and thermodynamic quantities are treated on an equal footing. The second law of information thermodynamics serves as one of the fundamental principles of physics of information processing, which would be useful for designing and controlling nanomachines and nanodevices in thermally fluctuating environments.