Second Law of Thermodynamics - Kensuke KOBAYASHI, Osaka University

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• published: 30 Jan 2013
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Second Law of Thermodynamics Kensuke KOBAYASHI, Osaka University Thermodynamics describes the connection between heat and work and the conversion of one into the other. Although thermodynamics is founded on a very few laws deduced from empirical facts, it successfully explains many phenomena associated with heat in a deductive, universal way. There are two central laws in thermodynamics: the first one is that, while energy exists in many forms such as heat, electrical energy, and chemical energy, the total amount of energy remains constant ("law of energy conservation"). The second one goes that heat never spontaneously flows from a cold substance to a hot substance ("law of increasing entropy"). Originally, thermodynamics was triggered by the development of steam engines in Industrial Revolution. The steam engine is a typical heat engine, which converts heat to mechanical work. By thinking about what lies in this conversion, physicists have established the above two laws. While the first one may be reasonably accepted, the second one looks mysterious because this predicts, in spite of the first law, that the conversion from heat to work is never 100% efficient, as entropy never decreases in a closed system. Therefore, the implication of the second law is long controversial. "Maxwell’s Demon" is the most famous example. It was proposed that Demon, who could watch and control the molecular movement, would break the second law. Does Demon truly cheat the second law? As another point of view, the irreversibility inheres in the second law. Why or how does the arrow of time proceed to only one direction? While thermodynamics originally describes physical laws for macroscopic objects, recently, thermodynamics in a small system attached to a heat bath is intensively studied, which enables researchers to address the above essential problems in a modern way. Two main developments are remarked. The first is the "fluctuation theorem", which exactly connects between the probabilities of entropy production and annihilation in a small system. Several equalities such as Jarzynski one and Crooks relation, which were also found in 1990's and are closely related to the above theorem, are being actively studied both theoretically and experimentally. The second is the experiment to demonstrate a Maxwell’s Demon in terms of thermodynamics incorporating information entropy. These recent approaches are definitely a major step forward for understanding more the second law of thermodynamics. Let us see how we can address it these days to go beyond it.

Second Law of Thermodynamics - Takahiro SAGAWA, Kyoto University

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• published: 30 Jan 2013
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Information Thermodynamics Takahiro SAGAWA, Kyoto University 1. Introduction 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 [1]. 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 [2]. 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. 5. Conclusion 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.

Second Law of Thermodynamics - Kensuke KOBAYASHI, Osaka University

• Report rights infringement
• published: 30 Jan 2013
• views: 102

Second Law of Thermodynamics Kensuke KOBAYASHI, Osaka University Thermodynamics describes the connection between heat and work and the conversion of one into the other. Although thermodynamics is founded on a very few laws deduced from empirical facts, it successfully explains many phenomena associated with heat in a deductive, universal way. There are two central laws in thermodynamics: the first one is that, while energy exists in many forms such as heat, electrical energy, and chemical energy, the total amount of energy remains constant ("law of energy conservation"). The second one goes that heat never spontaneously flows from a cold substance to a hot substance ("law of increasing entropy"). Originally, thermodynamics was triggered by the development of steam engines in Industrial Revolution. The steam engine is a typical heat engine, which converts heat to mechanical work. By thinking about what lies in this conversion, physicists have established the above two laws. While the first one may be reasonably accepted, the second one looks mysterious because this predicts, in spite of the first law, that the conversion from heat to work is never 100% efficient, as entropy never decreases in a closed system. Therefore, the implication of the second law is long controversial. "Maxwell’s Demon" is the most famous example. It was proposed that Demon, who could watch and control the molecular movement, would break the second law. Does Demon truly cheat the second law? As another point of view, the irreversibility inheres in the second law. Why or how does the arrow of time proceed to only one direction? While thermodynamics originally describes physical laws for macroscopic objects, recently, thermodynamics in a small system attached to a heat bath is intensively studied, which enables researchers to address the above essential problems in a modern way. Two main developments are remarked. The first is the "fluctuation theorem", which exactly connects between the probabilities of entropy production and annihilation in a small system. Several equalities such as Jarzynski one and Crooks relation, which were also found in 1990's and are closely related to the above theorem, are being actively studied both theoretically and experimentally. The second is the experiment to demonstrate a Maxwell’s Demon in terms of thermodynamics incorporating information entropy. These recent approaches are definitely a major step forward for understanding more the second law of thermodynamics. Let us see how we can address it these days to go beyond it.

Second Law of Thermodynamics - Takahiro SAGAWA, Kyoto University

• Report rights infringement
• published: 30 Jan 2013
• views: 267

Information Thermodynamics Takahiro SAGAWA, Kyoto University 1. Introduction 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 [1]. 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 [2]. 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. 5. Conclusion 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.