Cycle Symmetry, Limit Theorems, and Fluctuation Theorems for Diffusion Processes on the Circle

dc.contributor.authorGe, Haoen_US
dc.contributor.authorJia, Chenen_US
dc.contributor.authorJiang, Da-Quanen_US
dc.contributor.utdAuthorJia, Chenen_US
dc.date.accessioned2018-08-20T16:07:02Z
dc.date.available2018-08-20T16:07:02Z
dc.date.created2016-06-11en_US
dc.date.issued2018-08-20
dc.description.abstractCyclic structure and dynamics are of great interest in both the fields of stochastic processes and nonequilibrium statistical physics. In this paper, we find a new symmetry of the Brownian motion named as the quasi-time-reversal invariance. It turns out that such an invariance of the Brownian motion is the key to prove the cycle symmetry for diffusion processes on the circle, which says that the distributions of the forming times of the forward and backward cycles, given that the corresponding cycle is formed earlier than the other, are exactly the same. With the aid of the cycle symmetry, we prove the strong law of large numbers, functional central limit theorem, and large deviation principle for the sample circulations and net circulations of diffusion processes on the circle. The cycle symmetry is further applied to obtain various types of fluctuation theorems for the sample circulations, net circulation, and entropy production rate.en_US
dc.description.sponsorshipNSFC (No. 10901040, No. 21373021, No. 11271029, and No. 11171024)en_US
dc.identifier.bibliographicCitationGe, Hao, Chen Jia, and Da-Quan Jiang. 2017. "Cycle symmetry, limit theorems, and fluctuation theorems for diffusion processes on the circle." Stochastic Processes and Their Applications 127(6), doi:10.1016/j.spa.2016.09.011en_US
dc.identifier.issn0304-4149en_US
dc.identifier.issue6en_US
dc.identifier.urihttp://hdl.handle.net/10735.1/5968
dc.identifier.volume127en_US
dc.language.isoenen_US
dc.publisherElsevier Science BVen_US
dc.relation.urihttp://dx.doi.org/10.1016/j.spa.2016.09.011en_US
dc.rights©2016 Elsevier B.V.en_US
dc.sourceStochastic Processes and Their Applications
dc.subjectBessel functionsen_US
dc.subjectFree-energy differencesen_US
dc.subjectStochastic processesen_US
dc.subjectEntropyen_US
dc.subjectMarkov operatorsen_US
dc.subjectMathematicsen_US
dc.subjectNonequilibrium statistical mechanicsen_US
dc.titleCycle Symmetry, Limit Theorems, and Fluctuation Theorems for Diffusion Processes on the Circleen_US
dc.type.genrearticleen_US

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