Abstract
A Faraday isolator is shown to develop a temperature difference between its input and output, but still complies with the second law when all the heat carriers, in this case, photons are homogeneous and indistinguishable. This result is a consequence of the H-theorem which assumes homogeneity and indistinguishability of particles. However, when a thermal feedback path is added, in which heat carriers have physical properties different from the photons in the isolator, then a heterogeneous system is formed not covered by the H-theorem, and the second law is violated.
Highlights
Reciprocity in absorption and emission is a requirement of detailed balance and expressed by Kirchhoff law of radiation for any wavelength and for any direction.α (ω,θ,φ ) = ε (ω,θ,φ ) (1)In other words, the absorptivity α is equal to the emissivity ε for any value of frequency ω and polar coordinate angles θ and φ
The absorptivity α is equal to the emissivity ε for any value of frequency ω and polar coordinate angles θ and φ. This law is conventionally accepted, yet non-reciprocity of transmission and reflection has been the puzzlement [1] to scientists as it appears to violate the principle of detailed balance and the second law
This paper explores the limits of applicability of the second law
Summary
Reciprocity in absorption and emission is a requirement of detailed balance and expressed by Kirchhoff law of radiation for any wavelength and for any direction. The absorptivity α is equal to the emissivity ε for any value of frequency ω and polar coordinate angles θ and φ This law is conventionally accepted, yet non-reciprocity of transmission and reflection has been the puzzlement [1] to scientists as it appears to violate the principle of detailed balance and the second law. Wien [2] attempts to prove that Faraday isolators cannot violate the second law He describes a thought experiment involving two black bodies A and B separated by a Faraday isolator comprised of polarizers X and Y and a Faraday rotator R. The partial reduction of the rotator’s operation can be countered by increasing the length of the rotator to restore its function His second argument requires light to be asymmetrically absorbed by the rotator as a function of the orientations of the non-local polarizers. Eventually re-radiated to the cold object, thereby reestablishing detailed balance
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