Cycle representatives for the coarse-graining of systems driven into a non-equilibrium steady state

New Journal of Physics

Volumn 17, Issue 11, 2015, Pages

  Knoch, Fabian ^a   Speck, Thomas ^a  

^a JOHANNES GUTENBERG UNIVERSITY   (Germany)

Author keywords

coarse graining; networks; non equilibrium

Indexed keywords

ENTROPY; NETWORKS (CIRCUITS); STATISTICAL MECHANICS;

ATOMISTIC SIMULATIONS; COARSE GRAINED MODELS; COARSE GRAINING; MARKOV STATE MODELS; NON EQUILIBRIUM; NON-EQUILIBRIUM STEADY STATE; STANDARD ALGORITHMS; THERMAL EQUILIBRIUMS;

COMPLEX NETWORKS;

EID: 84951868452     PISSN: 13672630     EISSN: None     Source Type: Journal    
DOI: 10.1088/1367-2630/17/11/115004     Document Type: Article

References (40)

1. Müller-Plathe F 2002 Coarse-graining in polymer simulation: from the atomistic to the mesoscopic scale and back Chem. Phys. Chem. 3 754-69
2. Peter C and Kremer K 2009 Multiscale simulation of soft matter systems - from the atomistic to the coarse-grained level and back Soft Matter 5 4357-66
3. Öttinger H C 2007 Systematic coarse graining: four lessons and a caveat from nonequilibrium statistical mechanics MRS Bull. 32 936-40
4. Chodera J D, Singhal N, Pande V S, Dill K A and Swope W C 2007 Automatic discovery of metastable states for the construction of markov models of macromolecular conformational dynamics J. Chem. Phys. 126 155101
5. Noé F and Fischer S 2008 Transition networks for modeling the kinetics of conformational change in macromolecules Curr. Opin. Struct. Biol. 18 154-62
6. Prinz J H, Wu H, Sarich M, Keller B, Senne M, Held M, Chodera J D, Schütte C and Noé F 2011 Markov models of molecular kinetics: generation and validation J. Chem. Phys. 134 174105
7. Grabert H 1982 Projection Operator Techniques in Nonequilibrium Statistical Mechanics (Berlin: Springer)
8. Zwanzig R 2001 Nonequilibrium Statistical Mechanics
9. Hijón C, Español P, Vanden-Eijnden E and Delgado-Buscalioni R 2010 Mori-Zwanzig formalism as a practical computational tool Faraday Discuss. 144 301-22
10. Español P and Löwen H 2009 Derivation of dynamical density functional theory using the projection operator technique J. Chem. Phys. 131 244101
11. Wittkowski R, Löwen H and Brand H R 2013 Microscopic approach to entropy production J. Phys. A: Math. Theor. 46 355003
12. Schmidt M and Brader J M 2013 Power functional theory for Brownian dynamics J. Chem. Phys. 138 214101
13. Seifert U 2012 Stochastic thermodynamics, fluctuation theorems, and molecular machines Rep. Prog. Phys. 75 126001
14. Speck T, Mehl J and Seifert U 2008 Role of external flow and frame invariance in stochastic thermodynamics Phys. Rev. Lett. 100 178302
15. Andrieux D and Gaspard P 2006 Fluctuation theorems and the nonequilibrium thermodynamics of molecular motors Phys. Rev. E 74 011906
16. Andrieux D and Gaspard P 2007 Fluctuation theorem for currents and Schnakenberg network theory J. Stat. Phys. 127 107-31
17. Schmiedl T and Seifert U 2007 Optimal finite-time processes in stochastic thermodynamics Phys. Rev. Lett. 98 108301
18. Mehl J, Lander B, Bechinger C, Blickle V and Seifert U 2012 Role of hidden slow degrees of freedom in the fluctuation theorem Phys. Rev. Lett. 108 220601
19. Leonard T, Lander B, Seifert U and Speck T 2013 Stochastic thermodynamics of fluctuating density fields: non-equilibrium free energy differences under coarse-graining J. Chem. Phys. 139 204109
20. Puglisi A, Pigolotti S, Rondoni L and Vulpiani A 2010 Entropy production and coarse graining in Markov processes J. Stat. Mech. P05015
21. Altaner B and Vollmer J 2012 Fluctuation-preserving coarse graining for biochemical systems Phys. Rev. Lett. 108 228101
22. Rahav S and Jarzynski C 2007 Fluctuation relations and coarse-graining J. Stat. Mech. P09012
23. Esposito M 2012 Stochastic thermodynamics under coarse-graining Phys. Rev. E 85 041125
24. Altaner B, Grosskinsky S, Herminghaus S, Katthän L, Timme M and Vollmer J 2012 Network representations of nonequilibrium steady states: Cycle decompositions, symmetries, and dominant paths Phys. Rev. E 85 041133
25. Zimmermann E and Seifert U 2012 Efficiencies of a molecular motor: a generic hybrid model applied to the f 1 -atpase New J. Phys. 14 103023
26. Zimmermann E and Seifert U 2015 Effective rates from thermodynamically consistent coarse-graining of models for molecular motors with probe particles Phys. Rev. E 91 022709
27. Schnakenberg J 1976 Network theory of microscopic and macroscopic behavior of master equation systems Rev. Mod. Phys. 48 571
28. Hill T L 1989 Free Energy Transduction and Biochemical Cycle Kinetics (New York: Springer)
29. Zia R K P and Schmittmann B 2007 Probability currents as principal characteristics in the statistical mechanics of non-equilibrium steady states J. Stat. Mech. 2007 P07012
30. Polettini M 2015 Cycle/cocycle oblique projections on oriented graphs Lett. Math. Phys. 105 89-107
31. Barato A C and Seifert U 2015 Thermodynamic uncertainty relation for biomolecular processes Phys. Rev. Lett. 114 158101
32. Prinz J H, Wu H, Sarich M, Keller B, Senne M, Held M, Chodera J D, Schütte C and Noé F 2011 Markov models of molecular kinetics: generation and validation J. Chem. Phys. 134 174105
33. Conrad N D, Banisch R and Schütte C 2014 Modularity of Directed Networks: Cycle Decomposition Approach arXiv:1407.8039
34. Seifert U 2005 Entropy production along a stochastic trajectory and an integral fluctuation theorem Phys. Rev. Lett. 95 040602
35. Kalpazidou S 2006 Cycle Representations of Markov Processes (Berlin: Springer)
36. Jiang D Q, Qian M and Qian M P 2004 Mathematical Theory of Nonequilibrium Steady States (Berlin: Springer)
37. Volkmann L 1996 Fundamente der Graphentheorie Springer Lehrbuch Mathematik [Springer Mathematics Textbook] (Berlin: Springer)
38. Fortunato S 2010 Community detection in graphs Phys. Rep. 486 75-174
39. Newman M E 2004 Fast algorithm for detecting community structure in networks Phys. Rev. E 69 066133
40. Blondel V D, Guillaume J L, Lambiotte R and Lefebvre E 2008 Fast unfolding of communities in large networks J. Stat. Mech. 2008 P10008