Abstract
A linear non-Gaussian–Langevin equation is derived from microscopic dynamics by a systematic expansion. We generalize the conventional system size expansion for systems associated with thermal and athermal reservoirs, and find an explicit condition whereby the non-Gaussianity of athermal fluctuation becomes dominant with the violation of the central limit theorem. We also derive an inverse formula to infer the statistics of athermal bath from the statistics of the tracer particle. To demonstrate the utility of our formulation, we apply our expansion to a granular motor under viscous friction.
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References
E. Ben-Isaac, Y.K. Park, G. Popescu, F.L.H. Brown, N.S. Gov, Y. Shokef, Phys. Rev. Lett. 106, 238103 (2011)
N. Gov, Phys. Rev. Lett. 93, 268104 (2004)
P. Eshuis, K. van der Weele, D. Lohse, D. van der Meer, Phys. Rev. Lett. 104, 248001 (2010)
J. Talbot, R.D. Wildman, P. Viot, Phys. Rev. Lett. 107, 138001 (2011)
A. Gnoli, A. Petri, F. Dalton, G. Pontuale, G. Gradenigo, A. Sarracino, A. Puglisi, Phys. Rev. Lett. 110, 120601 (2013)
A. Gnoli, A. Puglisi, H. Touchette, Europhys. Lett. 102, 14002 (2013)
A. Gnoli, A. Sarracino, A. Puglisi, A. Petri, Phys. Rev. E 87, 052209 (2013)
J. Gabelli, B. Reulet, Phys. Rev. B 80, 161203(R) (2009)
A.M. Zaklikiewicz, Solid-State Electron. 43, 11 (1999)
Y.M. Blanter, M. Bu, D.P. Theh, U. De Gene, Phys. Rep. 336, 1 (2000)
J.P. Pekola, Phys. Rev. Lett. 93, 206601 (2004)
K. Kanazawa, T.G. Sano, T. Sagawa, H. Hayakawa, Phys. Rev. Lett. 114, 090601 (2015)
I. Eliazar, J. Klafter, J. Stat. Phys. 111, 739 (2003)
C. van den Broeck, J. Stat. Phys. 31, 467 (1983)
J. Łuczka, T. Czernik, P. Hanggi, Phys. Rev. E 56, 3968 (1997)
A. Baule, P. Sollich, Europhys. Lett. 97, 20001 (2012)
A. Baule, P. Sollich, Phys. Rev. E 87, 032112 (2013)
K. Sekimoto, Stochastic Energetics (Springer, Berlin, 2010)
K. Sekimoto, J. Phys. Soc. Jpn. 66, 1234 (1997)
K. Sekimoto, Prog. Theor. Phys. Suppl. 130, 17 (1998)
K. Kanazawa, T. Sagawa, H. Hayakawa, Phys. Rev. Lett. 108, 210601 (2012)
R. Strichartz, A Guide to Distribution Theory and Fourier Transforms (World Scientific, Singapore, 2008)
S. Albeveriob, B. Smii, Stoch. Process. Appl. 125, 1009 (2015)
B. Cleuren, R. Eichhorn, J. Stat. Mech. (2008) P10011
L.O. Gálvez, D. van der Meer, J. Stat. Mech. (2016) P043206
J.S. Olafsen, J.S. Urbach, Phys. Rev. E 60, 2468(R) (1999)
A.P. Prudnikov, Y.A. Brychkov, O.I. Marichev, Integrals and Series: More Special Functions, vol. 3 (Gordon and Breanch Science Publishers, Amsterdam, 1990)
T.G. Sano, K. Kanazawa, H. Hayakawa, Phys. Rev. E 94, 032910 (2016)
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Kanazawa, K. (2017). Microscopic Derivation of Linear Non-Gaussian Langevin Equation. In: Statistical Mechanics for Athermal Fluctuation. Springer Theses. Springer, Singapore. https://doi.org/10.1007/978-981-10-6332-9_7
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DOI: https://doi.org/10.1007/978-981-10-6332-9_7
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