Chin. Phys. Lett.  2013, Vol. 30 Issue (7): 070201    DOI: 10.1088/0256-307X/30/7/070201
GENERAL |
Dynamical Decomposition of Markov Processes without Detailed Balance
AO Ping1,3**, CHEN Tian-Qi2, SHI Jiang-Hong2
1Key Laboratory of Systems Biomedicine of Ministry of Education, Shanghai Center for Systems Biomedicine, Shanghai Jiao Tong University, Shanghai 200240
2Department of Computer Science and Engineering, Shanghai Jiao Tong University, Shanghai 200240
3Department of Physics, Shanghai Jiao Tong University, Shanghai 200240
Cite this article:   
AO Ping, CHEN Tian-Qi, SHI Jiang-Hong 2013 Chin. Phys. Lett. 30 070201
Download: PDF(619KB)  
Export: BibTeX | EndNote | Reference Manager | ProCite | RefWorks
Abstract We introduce a dynamical decomposition view in dealing with Markov processes without detailed balance. This work generalizes a previous decomposition framework on continuous-state Markov processes and explicitly gives its correspondence in discrete-state case. We investigate the dynamical roles of decomposed parts by studying the evolution of relative-entropy-like functions. We find a special definition of relative entropy to unify the dynamical roles played by the detailed balance part and the breaking detailed balance part. The evolution of the relative entropy naturally bounds the convergence of the process.
Received: 20 March 2013      Published: 21 November 2013
PACS:  02.50.Ga (Markov processes)  
  74.40.Gh (Nonequilibrium superconductivity)  
  02.50.Fz (Stochastic analysis)  
TRENDMD:   
URL:  
https://cpl.iphy.ac.cn/10.1088/0256-307X/30/7/070201       OR      https://cpl.iphy.ac.cn/Y2013/V30/I7/070201
Service
E-mail this article
E-mail Alert
RSS
Articles by authors
AO Ping
CHEN Tian-Qi
SHI Jiang-Hong
[1] Binder K and Heermann D 2010 Monte Carlo Simulation Stat. Phys. 5th edn (Berlin: Springer-Verlag)
[2] Qian H 2010 J. Stat. Phys. 141 990
[3] Wang J, Xu L and Wang E K 2008 Proc. Natl. Acad. Sci. U.S.A. 105 12271
[4] Ao P, Galas D, Hood L and Zhu X M 2008 Med. Hypotheses 70 678
[5] Jiao S Y and Ao P 2012 BMC Syst. Biol. 6 S10
[6] Zhou D and Qian H 2011 Phys. Rev. E 84 031907
[7] Kim J W, Lee J S, Robinson P A and Jeong D U 2009 Phys. Rev. Lett. 102 178104
[8] Zhu X M, Yin L, Hood L and Ao P 2004 Funct. Integr. Genomics 4 188
[9] Jiang D Q, Qian M and Qian M P 2004 Mathematical Theory of Nonequilibrium Steady States: On the Frontier of Probability and Dynamical Systems (Lect. Notes Math.) vol 1833 (Berlin: Springer-Berlin)
[10] Zia R K P and Schmittmann B 2007 J. Stat. Mech. 2007 P07012
[11] Kwon C, Ao P and Thouless D J 2005 Proc. Natl. Acad. Sci. USA 102 13029
[12] Yin L and Ao P 2006 J. Phys. A: Math. Gen. 39 8593
[13] Ao P 2008 Commun. Theor. Phys. 49 1073
[14] Xing J 2010 J. Phys. A: Math. Theor. 43 375003
[15] Shi J, Chen T, Yuan R, Yuan B and Ao P 2012 J. Stat. Phys. 148 579
[16] Yuan R and Ao P 2012 J. Stat. Mech. 2012 P07010
[17] Suwa H and Todo S 2010 Phys. Rev. Lett. 105 120603
[18] Xu W, Yuan B and Ao P 2011 Chin. Phys. Lett. 28 050201
[19] Cover T M and Thomas J A 1991 Elements of Information Theory (New York: Wiley-Interscience)
[20] Xing X S 2006 Sci. Chin. G 49 1
[21] van Kampen N G 2007 Stochastic Processes Phys. Chem. 3rd edn (Amsterdam: North Holland)
[22] Rao C R 1982 Sankhyā: Indian J. Stati. Ser. A 44 1
[23] Beck C 2009 Contemp. Phys. 50 495
[24] Du J L 2010 Chin. Phys. B 19 040501
[25] Diaconis P and Coste S L 1996 Ann. Appl. Probab. 6 695
[26] Fill J A 1991 Ann. Appl. Probab. 1 62
[27] Qian H 2012 arXiv:1204.6496 [math-ph]
[28] Santillán M and Qian H 2013 Physica A 392 123
Related articles from Frontiers Journals
[1] XIE Yan-Bo, LI Yu-Jian, LI Ming, XI Zhen-Dong, WANG Bing-Hong. An Exact Numerical Approach to Calculate the First Passage Time for General Random Walks on a Network[J]. Chin. Phys. Lett., 2013, 30(11): 070201
[2] XU Hong, SHI Ding-Hua. Stability of the BA Network: a New Approach to Rigorous Proof[J]. Chin. Phys. Lett., 2009, 26(3): 070201
Viewed
Full text


Abstract