The Appearance of Regular Fluxes Without Gradients
The central topic of the present section is transport phenomena in spatially periodic systems in the absence of displacing macroscopic forces (gradients). A complete solution of the problem must include an understanding of the effect’s essence, the establ
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The Appearance of Regular Fluxes Without Gradients
The central topic of the present section is transport phenomena in spatially periodic systems in the absence of displacing macroscopic forces (gradients). A complete solution of the problem must include an understanding of the effect’s essence, the establishment of the conditions at which a gradient-free current is possible, and a quantitative investigation of the models and realistic systems where the effect can be observed.
8.1 Introduction Mass, energy, and charge transport is the basis of very diverse phenomena in nature. On the macroscopic level one should distinguish between convective and diffusive transport. The characteristic feature of the former is directed motion, generated by gradients of different fields: force, temperature, concentration, etc. At the same time, directed motion is absent in diffusive transport, which is generated by random collisions. The ambitious task to obtain useful work (or directed motion) from fluctuations, in spite of seemingly overwhelming difficulties, has long attracted the attention of enthusiasts. According to statistics, for every proposal of a perpetuum mobile of first kind there are eight projects of the second kind. The principal difficulty is in the fact that useful work cannot be extracted from thermal equilibrium fluctuations. Such a machine would violate the second law of thermodynamics. There are several equivalent formulations of the second law. The very term as well as the first formulation is credited to Clausius [1]: a process where heat spontaneously transits from the colder bodies to the warmer ones is impossible. The term “spontaneously” should be understood in the sense that the transition cannot be realized with the help of any setups without some other changes in nature. In other words, it is impossible to realize a process, the only outcome of which would be heat transfer from a colder body to a warmer one. If, in violation of the Klausius © Springer International Publishing Switzerland 2017 Y. Bolotin et al., Chaos: Concepts, Control and Constructive Use, Understanding Complex Systems, DOI 10.1007/978-3-319-42496-5_8
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8 The Appearance of Regular Fluxes Without Gradients
formulation, such a process appeared to be possible, it would allow one to obtain two reservoirs with different temperatures by the simple division of one reservoir in two parts and the transferring of heat from one part to another. In its turn it would allow one to perform the Carno cycle and to obtain mechanical work with the help of a periodically acting machine at the cost of internal energy—in the end, at the cost of one thermal reservoir. As this is impossible, in nature it is impossible to realize a process, the only result of which would be load lifting (i.e., mechanical work) executed due to the cooling of the thermal reservoir. The latter represents the formulation of the second law of thermodynamics by W. Thomson. It is easy to see that the two formulations are interrelated. The mechanical work obtained by cool
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