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A version of the second law of thermodynamics states that one cannot lower the energy of an isolated system by a cyclic operation.
1929
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One of the authors (H.T.) has an unpublished (premature) work ( arXiv:cond-mat/0011321v2
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Recently Ikeda, Sakumichi, Polkovnikov and Ueda (preprint, arXiv:1303.5471
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J. Kurchan, arXiv:cond-mat/0007360
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H. Tasaki, arXiv:cond-mat/0009244
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An essential advantage of this formulation of the second law is that it does not refer to the entropy. Recall that, in thermodynamics, the entropy is not a directly observable quantity, while the change in the energy is. By focusing only on the energy, we can develop a microscopic theory that is free from arbitrariness of the (microscopic) definition of entropy
Cited in the paper.
The cyclicity is assumed only for simplicity. The initial and the final Hamiltonians may be distinct (as in Hal2000 ), but then the setting becomes complicated
Cited in the paper.
N. Linden, S. Popescu, A. J. Short, A. Winter, Phys. Rev. E 79
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S. Goldstein, J. L. Lebowitz, C. Mastrodonato, R. Tumulka, N. Zanghì, Phys. Rev. E 81
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T. Sagawa, in Lectures on Quantum Computing, Thermodynamics and Statistical Physics
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