2016
DOI: 10.1214/15-aap1152
|View full text |Cite
|
Sign up to set email alerts
|

Cycle symmetries and circulation fluctuations for discrete-time and continuous-time Markov chains

Abstract: In probability theory, equalities are much less than inequalities. In this paper, we find a series of equalities which characterize the symmetry of the forming times of a family of similar cycles for discrete-time and continuous-time Markov chains. Moreover, we use these cycle symmetries to study the circulation fluctuations for Markov chains. We prove that the empirical circulations of a family of cycles passing through a common state satisfy a large deviation principle with a rate function which has an highl… Show more

Help me understand this report

Search citation statements

Order By: Relevance

Paper Sections

Select...
1
1
1

Citation Types

1
22
0

Year Published

2018
2018
2024
2024

Publication Types

Select...
7

Relationship

0
7

Authors

Journals

citations
Cited by 20 publications
(23 citation statements)
references
References 43 publications
1
22
0
Order By: Relevance
“…Importantly, the SCGF for the edge currents, and of any linear contraction of them, is a convex function. An accessible proof of this fact can be found in [105]). Finally, the contraction principle in large deviation theory allows to derive the SCGF of a coarse-grained observable from that of more specialized observables.…”
Section: Time-integrated Currentsmentioning
confidence: 85%
See 1 more Smart Citation
“…Importantly, the SCGF for the edge currents, and of any linear contraction of them, is a convex function. An accessible proof of this fact can be found in [105]). Finally, the contraction principle in large deviation theory allows to derive the SCGF of a coarse-grained observable from that of more specialized observables.…”
Section: Time-integrated Currentsmentioning
confidence: 85%
“…In view of the explicit form of the generators Eqs. (105,114), we consider the minors obtained by removing the first row and column and the second row and column, and notice that…”
Section: Thermodynamics: the Effective Affinitymentioning
confidence: 99%
“…Thus, the distribution of the current along bridges with fixed frenesy Φ T (iso-frenetic bridges) is asymmetric with respect to change of sign of the current and its asymmetry is independent on the level of frenesy. which implies the cycle fluctuation relation for currents P (J T )/P (−J T ) = e (∆S/kB)J T [89,90].…”
Section: Frenetic Information About the Currentmentioning
confidence: 99%
“…is the net occurrence of cycle c per unit time, and J c >0 if and only if γ ( c) >1. The number of occurrences ν c (τ) of the forward cycle c time τ satisfies the detailed fluctuation theorem[4,45] any integer k. It follows that[4,45] …”
mentioning
confidence: 95%
“…net fluxes of all of these transported molecules go against the temperature gradient. This does not violate the Second Law of Thermodynamics.The number of occurrences ν i (τ) of counterclockwise cycle i (i=a, b, c) infigure 5along the stochastic trajectory up to time τ satisfies the detailed fluctuation theorem[4,45] …”
mentioning
confidence: 99%