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Continuous State Space Models

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Non-equilibrium Energy Transformation Processes

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Abstract

In this section we illustrate the difference between the two work definitions (2.44) and (2.53) on two specific models. Specifically, we demonstrate validity of the individual formulas presented in Sect. 2.2.3. Moreover, we introduce two examples of externally controlled parameters \({{\varvec{Y}}}(t)\) used in single molecule experiments [14].

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References

  1. Collin, D., Ritort, F., Jarzynski, C., et al. (2005). Verification of the Crooks fluctuation theorem and recovery of RNA folding free energies. Nature, 473, 231. http://dx.doi.org/10.1038/nature04061M3.

  2. Ritort, F. (2006). Single-molecule experiments in biological physics: Methods and applications. Journal of Physics: Condensed Matter, 18(32), R531. http://stacks.iop.org/0953-8984/18/i=32/a=R01.

  3. Ritort, F. (2008). Nonequilibrium fluctuations in small systems: From physics to biology. In A. Rice Stuart (Ed.), Advances in chemical physics (Vol. 137, pp. 31–123). Hoboken: John Wiley & Sons Inc. ISBN 9780470238080, doi:10.1002/9780470238080.ch2.

  4. Alemany, A., Ribezzi, M., & Ritort, F. (2011). Recent progress in fluctuation theorems and free energy recovery. AIP Conference Proceedings, 1332(1), 96–110. doi:10.1063/1.3569489, http://link.aip.org/link/?APC/1332/96/1.

  5. Mazonka, O., & Jarzynski, C. (1999). Exactly solvable model illustrating far-from-equilibrium predictions. eprint arXiv:cond-mat/9912121, December 1999.

  6. Holubec, V., Chvosta, P., & Ryabov, A. (2010). Four exactly solvable examples in non-equilibrium thermodynamics of small systems. In Thermodynamics (pp. 153–176). InTech. doi:10.5772/13374, http://www.intechopen.com/books/thermodynamics.

  7. Engel, A. (2009). Asymptotics of work distributions in nonequilibrium systems. Physical Review E, 80, 021120. doi:10.1103/PhysRevE.80.021120.

  8. Nickelsen, D., & Engel, A. (2011). Asymptotics of work distributions: The pre-exponential factor. The European Physical Journal B, 82, 207–218. ISSN 1434–6028, doi:10.1140/epjb/e2011-20133-y.

  9. Speck, T. (2011). Work distribution for the driven harmonic oscillator with time-dependent strength: Exact solution and slow driving. Journal of Physics A: Mathematical and Theoretical, 44(30), 305001. http://stacks.iop.org/1751-8121/44/i=30/a=305001.

  10. Ryabov, A., Dierl, M., Chvosta, P., et al. (2013). Work distribution in a time-dependent logarithmic-harmonic potential: Exact results and asymptotic analysis. Journal of Physics A: Mathematical and Theoretical, 46(7), 075002. http://stacks.iop.org/1751-8121/46/i=7/a=075002.

  11. Wilcox, R. M. (1967). Exponential operators and parameter differentiation in quantum physics. Journal of Mathematical Physics, 8(4), 962–982. doi:10.1063/1.1705306, http://link.aip.org/link/?JMP/8/962/1.

  12. Wolf, F. (1988). Lie algebraic solutions of linear Fokker-Planck equations. Journal of Mathematical Physics, 29(2), 305–307. doi:10.1063/1.528067, http://link.aip.org/link/?JMP/29/305/1.

  13. Baule, A., & Cohen, E. G. D. (2009). Fluctuation properties of an effective nonlinear system subject to Poisson noise. Physical Review E, 79, 030103. doi:10.1103/PhysRevE.79.030103.

  14. Van Kampen, N. (2011). Stochastic processes in physics and chemistry. North-Holland Personal Library. Amsterdam: Elsevier Science. ISBN 9780080475363, http://books.google.cz/books?id=N6II-6HlPxEC.

  15. Gillespie, D. T. (1992). Markov processes: An introduction for physical scientist. San Diego: Academic press, Inc.

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Correspondence to Viktor Holubec .

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Holubec, V. (2014). Continuous State Space Models. In: Non-equilibrium Energy Transformation Processes. Springer Theses. Springer, Cham. https://doi.org/10.1007/978-3-319-07091-9_4

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