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Oscillations and multiscale dynamics in a closed chemical reaction system: Second law of thermodynamics and temporal complexity

J. Chem. Phys. 129, 154505 (2008); doi:10.1063/1.2995855

Published 16 October 2008

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Yongfeng Li,1 Hong Qian,2 and Yingfei Yi3
1School of Mathematics, Georgia Institute of Technology, Atlanta, Georgia 30332, USA
2Department of Applied Mathematics, University of Washington, Seattle, Washington 98195, USA
3School of Mathematics, Georgia Institute of Technology, Atlanta, Georgia 30332, USA and College of Mathematics, Jilin University, Changchun 130012, People's Republic of China
We investigate the oscillatory reaction dynamics in a closed isothermal chemical system: the reversible Lotka–Volterra model. The second law of thermodynamics dictates that the system ultimately reaches an equilibrium. Quasistationary oscillations are analyzed while the free energy of the system serves as a global Lyapunov function of the dissipative dynamics. A natural distinction between regions near and far from equilibrium in terms of the free energy can be established. The dynamics is analogous to a nonlinear mechanical system with time-dependent increasing damping. Near equilibrium, no oscillation is possible as dictated by Onsager's reciprocal symmetry relation. We observe that while the free energy decreases in the closed system's dynamics, it does not follow the steepest descending path. ©2008 American Institute of Physics
History: Received 15 May 2008; accepted 15 September 2008; published 16 October 2008
Permalink: http://link.aip.org/link/?JCPSA6/129/154505/1
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KEYWORDS and PACS

Keywords
PACS
  • 82.60.Hc
    Chemical equilibria and equilibrium constants
  • 82.20.-w
    Chemical kinetics and dynamics
  • YEAR: 2008

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PUBLICATION DATA

ISSN:
0021-9606 (print)   1089-7690 (online)
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REFERENCES (36)
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