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9
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85039595843
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Free Energy Transduction and Biochemical Cycle Kinetics (Springer-Verlag, New York, 1995);, Free Energy Transduction in Biology (Academic, New York, 1977)
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T.L. Hill, Free Energy Transduction and Biochemical Cycle Kinetics (Springer-Verlag, New York, 1995);Free Energy Transduction in Biology (Academic, New York, 1977);
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Hill, T.L.1
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10
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85039594525
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Nature (London) 299, 84 (1982).
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(1982)
Nature (London)
, vol.299
, pp. 84
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20
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85039595251
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e-print physics/0007014
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H. Qian, e-print physics/0007014.
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Qian, H.1
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22
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0034311689
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Equation (4) can be viewed as the relative entropy between distribution (Formula presented) and its time reversal (Formula presented) See D.-Q. Jiang, M. Qian, and M.-P. Qian, Commun. Math. Phys. 214, 389 (2000);
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(2000)
Commun. Math. Phys.
, vol.214
, pp. 389
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Jiang, D.-Q.1
Qian, M.2
Qian, M.-P.3
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24
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85039589369
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See 6 for an implicit proof of the symmetry. Let the stationary Markov jump process, (Formula presented) starting at (Formula presented) completing cycle (Formula presented) (Formula presented) times up to t, and (Formula presented) times return to (Formula presented) by noncircular paths. Then (Formula presented) For large t, (Formula presented) are expected to be t independent
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See 6 for an implicit proof of the symmetry. Let the stationary Markov jump process, (Formula presented) starting at (Formula presented) completing cycle (Formula presented) (Formula presented) times up to t, and (Formula presented) times return to (Formula presented) by noncircular paths. Then (Formula presented) For large t, (Formula presented) are expected to be t independent.
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29
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0346242489
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G.-L. Gong and M.-P. Qian, Sci. China, Ser. A: Math., Phys., Astron. Technol. Sci. 41, 1017 (1998).
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(1998)
Sci. China, Ser. A: Math., Phys., Astron. Technol. Sci.
, vol.41
, pp. 1017
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Gong, G.-L.1
Qian, M.-P.2
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32
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85039589339
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Heuristically, at (Formula presented) with small (Formula presented) the approximated solution to Eq. (6) is (Formula presented) from which it is easy to show (Formula presented) analogous to Eq. (2)
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Heuristically, at (Formula presented) with small (Formula presented) the approximated solution to Eq. (6) is (Formula presented) from which it is easy to show (Formula presented) analogous to Eq. (2).
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34
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85039599529
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Note also (Formula presented) where (Formula presented) and (Formula presented) are Onsager’s force and flux. This is a special case of Eq. (9). This connection to Onsager’s work is well-known to T.L. Hill and can be found in his work on biological free energy transduction 4
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Note also (Formula presented) where (Formula presented) and (Formula presented) are Onsager’s force and flux. This is a special case of Eq. (9). This connection to Onsager’s work is well-known to T.L. Hill and can be found in his work on biological free energy transduction 4.
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35
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36149006492
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his paper dissipation function Φ=EPR/2, and (Formula presented) is HDR. Hence (Formula presented) is our EPR/2, which is the functional for PLD. Onsager also discussed the case when (Formula presented) Under this condition, the system cannot be stationary. Hence this portion of his work only applies to a nonstationary transient, which is outside the scope of this paper
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L. Onsager, Phys. Rev. 37, 405 (1931). In his paper dissipation function Φ=EPR/2, and (Formula presented) is HDR. Hence (Formula presented) is our EPR/2, which is the functional for PLD. Onsager also discussed the case when (Formula presented) Under this condition, the system cannot be stationary. Hence this portion of his work only applies to a nonstationary transient, which is outside the scope of this paper.
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(1931)
Phys. Rev.
, vol.37
, pp. 405
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Onsager, L.1
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