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.

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