Methods are presented to evaluate the entropy production rate in stochastic reactive systems. These methods are shown to be consistent with known results from nonequilibrium chemical thermodynamics. Moreover, it is proved that the time average of the entropy production rate can be decomposed into the contributions of the cycles obtained from the stoichiometric matrix in both stochastic processes and deterministic systems. These methods are applied to a complex reaction network constructed on the basis of Rössler’s reinjection principle and featuring chemical chaos.
REFERENCES
1.
O. E.
Rössler
, Z. Naturforsch. A
31
, 1168
(1976
). 2.
O. E.
Rössler
, Phys. Lett. A
57
, 397
(1976
). 3.
O. E.
Rössler
, Z. Naturforsch. A
31
, 1664
(1976
). 4.
O. E.
Rössler
, “Continuous chaos,” in Synergetics: A Workshop, edited by H. Haken (Springer, New York, 1977), pp. 184–199.5.
O. E.
Rössler
, Ann. N.Y. Acad. Sci.
316
, 376
(1979
). 6.
O. E.
Rössler
, Phys. Lett. A
71
, 155
(1979
). 7.
O. E.
Rössler
, Z. Naturforsch. A
31
, 259
(1976
). 8.
O. E.
Rössler
and K.
Wegmann
, Nature
271
, 89
(1978
). 9.
D.
Ruelle
, Trans. New York Acad. Sci.
35
, 66
(1973
). 10.
J. L.
Hudson
, M.
Hart
, and D.
Marinko
, J. Chem. Phys.
71
, 1601
(1979
). 11.
J. L.
Hudson
and J. C.
Mankin
, J. Chem. Phys.
74
, 6171
(1981
). 12.
J. S.
Turner
, J.-C.
Roux
, W. D.
McCormick
, and H. L.
Swinney
, Phys. Lett. A
85
, 9
(1981
). 13.
R. H.
Simoyi
and A.
Wolf and H. L. Swinney
, Phys. Rev. Lett.
49
, 245
(1982
). 14.
H. L.
Swinney
, Physica D
7
, 3
(1983
). 15.
I. R.
Epstein
, Physica D
7
, 47
(1983
). 16.
J.-C.
Roux
, Physica D
7
, 57
(1983
). 17.
J.-C.
Roux
, R. H.
Simoyi
, and H. L.
Swinney
, Physica D
8
, 257
(1983
). 18.
19.
F.
Argoul
, A.
Arnéodo
, and P.
Richetti
, Phys. Lett. A
120
, 269
(1987
). 20.
21.
I. R.
Epstein
and J. A.
Pojman
, An Introduction to Nonlinear Chemical Dynamics
(Oxford University Press
, New York
, 1998
).22.
K.-D.
Willamowski
and O. E.
Rössler
, Z. Naturforsch. A
35
, 317
(1980
). 23.
B. D.
Aguda
and B. L.
Clarke
, J. Chem. Phys.
89
, 7428
(1988
). 24.
P.
Gaspard
and G.
Nicolis
, J. Stat. Phys.
31
, 499
(1983
). 25.
N.
Samardzija
, L. D.
Greller
, and E.
Wasserman
, J. Chem. Phys.
90
, 2296
(1989
). 26.
X.-G.
Wu
and R.
Kapral
, Phys. Rev. Lett.
70
, 1940
(1993
). 27.
J.
Güémez
and M. A.
Matías
, Phys. Rev. E
48
, R 2351
(1993
). 28.
P.
Geysermans
and G.
Nicolis
, J. Chem. Phys.
99
, 8964
(1993
). 29.
P.
Geysermans
and F.
Baras
, J. Chem. Phys.
105
, 1402
(1996
). 30.
V.
Voorsluijs
and Y.
De Decker
, Physica D
335
, 1
(2016
). 31.
J. M.
Garcia-Fernández
, J. M.
Nieto-Villar
, and J.
Rieumont-Briones
, Phys. Scr.
53
, 643
(1996
). 32.
J. W.
Stucki
and R.
Urbanczik
, Z. Naturforsch. A
60
, 599
(2005
). 33.
T.
De Donder
and P.
Van Rysselberghe
, Affinity
(Stanford University Press
, Menlo Park, CA
, 1936
).34.
I.
Prigogine
, Introduction to Thermodynamics of Irreversible Processes
(Wiley
, New York
, 1967
).35.
G.
Nicolis
, Rep. Prog. Phys.
42
, 225
(1979
). 36.
37.
D.
Kondepudi
and I.
Prigogine
, Modern Thermodynamics: From Heat Engines to Dissipative Structures
(Wiley
, Chichester
, 1998
).38.
P. H.
Richter
, P.
Rehmus
, and J.
Ross
, Prog. Theor. Phys.
66
, 385
(1981
). 39.
J.-L.
Luo
, C.
Van den Broeck
, and G.
Nicolis
, Z. Phys. B Condens. Matter
56
, 165
(1984
). 40.
C. Y.
Mou
, J.-L.
Luo
, and G.
Nicolis
, J. Chem. Phys.
84
, 7011
(1986
). 41.
C.
Van den Broeck
, “Stochastic thermodynamics,” in Self-Organization by Nonlinear Irreversible Processes, edited by W. Ebeling and H. Ulbricht (Springer, Berlin, 1986), pp. 57–61.42.
J. L.
Lebowitz
and H.
Spohn
, J. Stat. Phys.
95
, 333
(1999
). 43.
P.
Gaspard
, J. Chem. Phys.
120
, 8898
(2004
). 44.
D.
Andrieux
and P.
Gaspard
, J. Chem. Phys.
121
, 6167
(2004
). 45.
D.
Andrieux
and P.
Gaspard
, J. Stat. Phys.
127
, 107
(2007
). 46.
D.
Andrieux
and P.
Gaspard
, J. Chem. Phys.
128
, 154506
(2008
). 47.
D.
Andrieux
and P.
Gaspard
, Phys. Rev. E
77
, 031137
(2008
). 48.
H.
Tomita
and M. M.
Sano
, Prog. Theor. Phys.
119
, 515
(2008
). 49.
U.
Seifert
, Phys. Rev. Lett.
95
, 040602
(2005
). 50.
U.
Seifert
, Eur. J. Phys. E
34
, 26
(2011
). 51.
U.
Seifert
, Rep. Prog. Phys.
75
, 126001
(2012
). 52.
M.
Esposito
and C.
Van den Broeck
, Phys. Rev. Lett.
104
, 090601
(2010
). 53.
M.
Esposito
and C.
Van den Broeck
, Phys. Rev. E
82
, 011143
(2010
). 54.
M.
Esposito
and C.
Van den Broeck
, Phys. Rev. E
82
, 011144
(2010
). 55.
M.
Esposito
, Phys. Rev. E
85
, 041125
(2012
). 56.
C.
Van den Broeck
, “Stochastic thermodynamics: A brief introduction,” in Proceedings of the International School of Physics Enrico Fermi,” Physics of Complex Colloids Vol. 184, edited by C. Bechinger, F. Sciortino, and P. Ziherl (IOS Press, Amsterdam, 2013).57.
C.
Van den Broeck
and M.
Esposito
, Physica A
418
, 6
(2015
). 58.
M.
Polettini
, A.
Wachtel
, and M.
Esposito
, J. Chem. Phys.
143
, 184103
(2015
). 59.
R.
Rao
and M.
Esposito
, New J. Phys.
20
, 023007
(2018
). 60.
R.
Rao
and M.
Esposito
, J. Chem. Phys.
149
, 245101
(2018
). 61.
T. J.
Xiao
, Z.
Hou
, and H.
Xin
, J. Chem. Phys.
129
, 114506
(2008
). 62.
T. J.
Xiao
, Z.
Hou
, and H.
Xin
, J. Phys. Chem. B
113
, 9316
(2009
). 63.
T. J.
Xiao
and Z.
Hou
, Sci. Chin. Chem.
53
, 396
(2010
). 64.
T.
Rao
, T. J.
Xiao
, and Z.
Hou
, J. Chem. Phys.
134
, 214112
(2011
). 65.
T. J.
Xiao
and Y.
Zhou
, Chin. J. Chem. Phys.
31
, 61
(2018
). 66.
Y.
De Decker
, Physica A
428
, 178
(2015
). 67.
Y.
De Decker
, J.-F.
Derivaux
, and G.
Nicolis
, Phys. Rev. E
93
, 042127
(2016
). 68.
J. M.
Horowitz
, J. Chem. Phys.
143
, 044111
(2015
). 69.
70.
F.
Schlögl
, Z. Phys.
248
, 446
(1971
). 71.
F.
Schlögl
, Z. Phys.
253
, 147
(1972
). 72.
G.
Nicolis
and I.
Prigogine
, Proc. Natl. Acad. Sci. U.S.A.
68
, 2102
(1971
). 73.
G.
Nicolis
, J. Stat. Phys.
6
, 195
(1972
). 74.
G.
Nicolis
and I.
Prigogine
, Self-Organization in Nonequilibrium Systems
(Wiley
, New York
, 1977
).75.
M.
Polettini
and M.
Esposito
, J. Chem. Phys.
141
, 024117
(2014
). 76.
R.
Rao
and M.
Esposito
, Phys. Rev. X
6
, 041064
(2016
). 77.
78.
A.
Wachtel
, R.
Rao
, and M.
Esposito
, New J. Phys.
20
, 042002
(2018
). 79.
C. W.
Gardiner
, Handbook of Stochastic Methods for Physics, Chemistry and the Natural Sciences
, 3rd ed. (Springer
, Berlin
, 2004
).80.
D. T.
Gillespie
, J. Comput. Phys.
22
, 403
(1976
). 81.
D. T.
Gillespie
, J. Phys. Chem.
81
, 2340
(1977
). 82.
J.
Schnakenberg
, Rev. Mod. Phys.
48
, 571
(1976
). 83.
N. G.
van Kampen
, Stochastic Processes in Physics and Chemistry
(North-Holland
, Amsterdam
, 1981
).84.
P.
Gaspard
, New J. Phys.
15
, 115014
(2013
). 85.
H.
Ge
and H.
Qian
, Phys. Rev. E
94
, 052150
(2016
). 86.
T. L.
Hill
, Free Energy Transduction and Biochemical Cycle Kinetics
(Dover
, New York
, 2005
).87.
A.
Blokhuis
, D.
Lacoste
, and P.
Gaspard
, J. Chem. Phys.
148
, 144902
(2018
). 88.
G.
Nicolis
, Introduction to Nonlinear Science
(Cambridge University Press
, Cambridge
, 1995
).89.
I. P.
Cornfeld
, S. V.
Fomin
, and Y. G.
Sinai
, Ergodic Theory
(Springer
, New York
, 1982
).90.
J.-P.
Eckmann
and D.
Ruelle
, Rev. Mod. Phys.
57
, 617
(1985
). © 2020 Author(s).
2020
Author(s)
You do not currently have access to this content.
