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A detailed balanced reaction network is sufficient but not necessary for its Markov chain to be detailed balanced
1.  Dept. of Mathematics, CSU San Marcos, 333 S. Twin Oaks Valley, San Marcos, CA 92096, United States 
References:
[1] 
D. F. Anderson, G. Craciun and T. G. Kurtz, Productform stationary distributions for deficiency zero chemical reaction networks, Bulletin of Mathematical Biology, 72 (2010), 19471970. doi: 10.1007/s1153801095174. 
[2] 
R. Aris, Prolegomena to the rational analysis of systems of chemical reactions, Archive for Rational Mechanics and Analysis, 19 (1965), 8199. doi: 10.1007/BF00282276. 
[3] 
R. Aris, Prolegomena to the rational analysis of systems of chemical reactions II. some addenda, Archive for Rational Mechanics and Analysis, 27 (1968), 356364. doi: 10.1007/BF00251438. 
[4] 
H. Casimir, Some aspects of Onsager's theory of reciprocal relations in irreversible processes, Il Nuovo Cimento, 6 (1949), 227231. doi: 10.1007/BF02780985. 
[5] 
A. Dickenstein and M. P. Millán, How far is complex balancing from detailed balancing?, Bulletin of Mathematical Biology, 73 (2011), 811828. doi: 10.1007/s1153801096117. 
[6] 
R. Durrett, Probability: Theory and examples, Cambridge University Press, 2010. doi: 10.1017/CBO9780511779398. 
[7] 
M. Feinberg, Necessary and sufficient conditions for detailed balancing in mass action systems of arbitrary complexity, Chemical Engineering Science, 44 (1989), 18191827. doi: 10.1016/00092509(89)851243. 
[8] 
M. Feinberg, Complex balancing in general kinetic systems, Archive for Rational Mechanics and Analysis, 49 (1972), 187194. 
[9] 
M. Feinberg, Lectures on Chemical Reaction Networks, Notes of lectures given at the Mathematics Research Center of the University of Wisconsin in 1979, available at http://www.crnt.osu.edu/LecturesOnReactionNetworks, 1979. 
[10] 
K. Gatermann, M. Eiswirth and A. Sensse, Toric ideals and graph theory to analyze Hopf bifurcations in mass action systems, Journal of Symbolic Computation, 40 (2005), 13611382. doi: 10.1016/j.jsc.2005.07.002. 
[11] 
J. Gunawardena, Chemical reaction network theory for insilico biologists, Notes available at http://vcp.med.harvard.edu/papers/crnt.pdf, 2003. 
[12] 
F. Horn, Necessary and sufficient conditions for complex balancing in chemical kinetics, Archive for Rational Mechanics and Analysis, 49 (1972), 172186. 
[13] 
F. Horn and R. Jackson, General mass action kinetics, Archive for Rational Mechanics and Analysis, 47 (1972), 81116. 
[14] 
B. Joshi, Complete characterization by multistationarity of fully open networks with one nonflow reaction, Applied Mathematics and Computation, 219 (2013), 69316945. doi: 10.1016/j.amc.2013.01.027. 
[15] 
B. Joshi and A. Shiu, Simplifying the Jacobian Criterion for precluding multistationarity in chemical reaction networks, SIAM Journal on Applied Mathematics, 72 (2012), 857876. doi: 10.1137/110837206. 
[16] 
B. Joshi and A. Shiu, Atoms of multistationarity in chemical reaction networks, Journal of Mathematical Chemistry, 51 (2013), 153178. 
[17] 
B. Joshi and A. Shiu, A survey of methods for deciding whether a reaction network is multistationary,, arXiv preprint, (). 
[18] 
F. Kelly, Reversibility and Stochastic Networks, Wiley, Chichester, 1979. 
[19] 
G. Lewis, A new principle of equilibrium, Proceedings of the National Academy of Sciences of the United States of America, 11 (1925), 179183. doi: 10.1073/pnas.11.3.179. 
[20] 
L. Onsager, Reciprocal relations in irreversible processes. I, Physical Review, 37 (1931), 405426. doi: 10.1103/PhysRev.37.405. 
[21] 
L. Paulevé, G. Craciun and H. Koeppl, Dynamical properties of discrete reaction networks, Journal of mathematical biology, 69 (2014), 5572. doi: 10.1007/s0028501306862. 
[22] 
P. Whittle, Systems in Stochastic Equilibrium, John Wiley & Sons, Inc., 1986. 
[23] 
E. Wigner, Derivations of Onsager's reciprocal relations, The Collected Works of Eugene Paul Wigner, A/4 (1997), 215218. doi: 10.1007/9783642590337_22. 
show all references
References:
[1] 
D. F. Anderson, G. Craciun and T. G. Kurtz, Productform stationary distributions for deficiency zero chemical reaction networks, Bulletin of Mathematical Biology, 72 (2010), 19471970. doi: 10.1007/s1153801095174. 
[2] 
R. Aris, Prolegomena to the rational analysis of systems of chemical reactions, Archive for Rational Mechanics and Analysis, 19 (1965), 8199. doi: 10.1007/BF00282276. 
[3] 
R. Aris, Prolegomena to the rational analysis of systems of chemical reactions II. some addenda, Archive for Rational Mechanics and Analysis, 27 (1968), 356364. doi: 10.1007/BF00251438. 
[4] 
H. Casimir, Some aspects of Onsager's theory of reciprocal relations in irreversible processes, Il Nuovo Cimento, 6 (1949), 227231. doi: 10.1007/BF02780985. 
[5] 
A. Dickenstein and M. P. Millán, How far is complex balancing from detailed balancing?, Bulletin of Mathematical Biology, 73 (2011), 811828. doi: 10.1007/s1153801096117. 
[6] 
R. Durrett, Probability: Theory and examples, Cambridge University Press, 2010. doi: 10.1017/CBO9780511779398. 
[7] 
M. Feinberg, Necessary and sufficient conditions for detailed balancing in mass action systems of arbitrary complexity, Chemical Engineering Science, 44 (1989), 18191827. doi: 10.1016/00092509(89)851243. 
[8] 
M. Feinberg, Complex balancing in general kinetic systems, Archive for Rational Mechanics and Analysis, 49 (1972), 187194. 
[9] 
M. Feinberg, Lectures on Chemical Reaction Networks, Notes of lectures given at the Mathematics Research Center of the University of Wisconsin in 1979, available at http://www.crnt.osu.edu/LecturesOnReactionNetworks, 1979. 
[10] 
K. Gatermann, M. Eiswirth and A. Sensse, Toric ideals and graph theory to analyze Hopf bifurcations in mass action systems, Journal of Symbolic Computation, 40 (2005), 13611382. doi: 10.1016/j.jsc.2005.07.002. 
[11] 
J. Gunawardena, Chemical reaction network theory for insilico biologists, Notes available at http://vcp.med.harvard.edu/papers/crnt.pdf, 2003. 
[12] 
F. Horn, Necessary and sufficient conditions for complex balancing in chemical kinetics, Archive for Rational Mechanics and Analysis, 49 (1972), 172186. 
[13] 
F. Horn and R. Jackson, General mass action kinetics, Archive for Rational Mechanics and Analysis, 47 (1972), 81116. 
[14] 
B. Joshi, Complete characterization by multistationarity of fully open networks with one nonflow reaction, Applied Mathematics and Computation, 219 (2013), 69316945. doi: 10.1016/j.amc.2013.01.027. 
[15] 
B. Joshi and A. Shiu, Simplifying the Jacobian Criterion for precluding multistationarity in chemical reaction networks, SIAM Journal on Applied Mathematics, 72 (2012), 857876. doi: 10.1137/110837206. 
[16] 
B. Joshi and A. Shiu, Atoms of multistationarity in chemical reaction networks, Journal of Mathematical Chemistry, 51 (2013), 153178. 
[17] 
B. Joshi and A. Shiu, A survey of methods for deciding whether a reaction network is multistationary,, arXiv preprint, (). 
[18] 
F. Kelly, Reversibility and Stochastic Networks, Wiley, Chichester, 1979. 
[19] 
G. Lewis, A new principle of equilibrium, Proceedings of the National Academy of Sciences of the United States of America, 11 (1925), 179183. doi: 10.1073/pnas.11.3.179. 
[20] 
L. Onsager, Reciprocal relations in irreversible processes. I, Physical Review, 37 (1931), 405426. doi: 10.1103/PhysRev.37.405. 
[21] 
L. Paulevé, G. Craciun and H. Koeppl, Dynamical properties of discrete reaction networks, Journal of mathematical biology, 69 (2014), 5572. doi: 10.1007/s0028501306862. 
[22] 
P. Whittle, Systems in Stochastic Equilibrium, John Wiley & Sons, Inc., 1986. 
[23] 
E. Wigner, Derivations of Onsager's reciprocal relations, The Collected Works of Eugene Paul Wigner, A/4 (1997), 215218. doi: 10.1007/9783642590337_22. 
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