# Martin Feinberg

**Martin Feinberg** is an American chemical engineer and mathematician known for his work in chemical reaction network theory.

## Life

Born in New York, Feinberg received his undergraduate degree in chemical engineering from the Cooper Union for the Advancement of Science and Art in 1962. A year later, he obtained his master's degree from Purdue University. In 1968, he received his PhD degree from Princeton University. The subject of his doctoral thesis was fluid mechanics and his advisor was William Schowalter. After completing the PhD, he went to work at the University of Rochester, Rochester, NY, where he was a professor of chemical engineering until 1997. He then moved to The Ohio State University, where he serves as Richard M. Morrow Professor of Chemical Engineering and Professor of Mathematics. Feinberg was a Member of the Editorial Board of the Archive for Rational Mechanics and Analysis from 1978-1991.

## Research

Together with F. J. M. Horn and Roy Jackson, Feinberg created chemical reaction network theory, a field of mathematics that connects the graphical and algebraic structure of chemical reaction networks with their dynamic behavior. He is best known for stating and proving the deficiency zero theorem (together with Horn and Jackson) and the deficiency one theorem. He has also articulated complete necessary and sufficient conditions for detailed balancing in mass-action systems. More recently, Feinberg has turned his attention to problems arising from biology. Together with Gheorghe Craciun, he developed the theory of injective reaction networks and explored its implications for biochemistry. A current research focus (together with Guy Shinar) is the application of chemical reaction network theory to questions of robustness in biochemical reaction networks. He has also worked with Richard Lavine on foundations of classical thermodynamics.

## Selected publications

- M. Feinberg, "Chemical reaction network structure and the stability of complex isothermal reactors: I. The deficiency zero and deficiency one theorems",
*Chemical Engineering Science*,**42**(10):2229–2268, 1987, doi 10.1016/0009-2509(87)80099-4 - M. Feinberg, "Necessary and sufficient conditions for detailed balancing in mass action systems of arbitrary complexity",
*Chemical Engineering Science*,**44**(9):1819–1827, 1989, doi 10.1016/0009-2509(89)85124-3 - P. M. Schlosser and M. Feinberg, "A theory of multiple steady states in isothermal homogeneous CFSTRs with many reactions",
*Chemical Engineering Science*,**49**(11):1749–1767, 1994, doi=10.1016/0009-2509(94)80061-8 - M. Feinberg, "The existence and uniqueness of steady states for a class of chemical reaction networks",
*Archive for Rational Mechanics and Analysis*,**132**(4):311–370, 1995, doi 10.1007/BF00375614 - G. Craciun, Y. Tang and M. Feinberg, "Understanding bistability in complex enzyme-driven reaction networks",
*Proc Natl Acad Sci U S A*,**103**(23):8697–8702, 2006, doi 10.1073/pnas.0602767103 - G. Shinar, U. Alon and M. Feinberg, "Sensitivity and robustness in chemical reaction networks",
*S. I. A. M. Journal on Applied Mathematics*,**69**(4):977–998, 2009, doi 10.1137/080719820 - G. Shinar and M. Feinberg, "Structural sources of robustness in biochemical reaction networks",
*Science*,**327**(5971):1389–1391, 2010, doi 10.1126/science.1183372 - M. Feinberg and R. B. Lavine, "Thermodynamics based on the Hahn-Banach theorem: the Clausius inequality",
*Archive for Rational Mechanics and Analysis*,**82**(3):203–293, 1983, doi 10.1007/BF00261935 - M. Feinberg and R. B. Lavine, "Foundations of the Clausius-Duhem Inequality", pp. 49–64 in
*New Perspectives in Thermodynamics*(editor James Serrin), Springer-Verlag, Berlin-Heidelberg-New York (1986).

## External links

## References

This article uses material from the Wikipedia article Martin Feinberg, which is released under the Creative Commons Attribution-ShareAlike Unported License 3.0.