Thermodynamics of Chemical Waves

Abstract

Chemical waves constitute a known class of dissipative structures emerging in reaction-diffusion systems. They play a crucial role in biology, spreading information rapidly to synchronize and coordinate biological events. We develop a rigorous thermodynamic theory of reaction-diffusion systems to characterize chemical waves. Our main result is the definition of the proper thermodynamic potential of the local dynamics as a nonequilibrium free energy density and establishing its balance equation. This enables us to identify the dynamics of the free energy, of the dissipation, and of the work spent to sustain the wave propagation. Two prototypical classes of chemical waves are examined. From a thermodynamic perspective, the first is sustained by relaxation towards equilibrium and the second by nonconservative forces generated by chemostats. We analytically study step-like waves, called wavefronts, using the Fisher-Kolmogorov equation as representative of the first class and oscillating waves in the Brusselator model as representative of the second. Given the fundamental role of chemical waves as message carriers in biosystems, our thermodynamic theory constitutes an important step toward an understanding of information transfers and processing in biology.

arXiv comment12 pages, 2 figures

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• Information Geometric Inequalities of Chemical Thermodynamics
• Reaction-Diffusion Waves Coupled with Membrane Curvature
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• Chemical Cloaking
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• Methods and Conversations in (Post)Modern Thermodynamics
• Nonequilibrium Thermodynamics of Non-Ideal Reaction-Diffusion Systems: Implications for Active Self-Organization
• The thermodynamic efficiency of the Lorenz system
• Precision and dissipation of a stochastic Turing pattern
• Open Questions on Nonequilibrium Thermodynamics of Chemical Reaction Networks
• Nonequilibrium thermodynamics of glycolytic traveling wave: Benjamin-Feir instability
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• Glycolytic Wave Patterns in a Simple Reaction-diffusion System with Inhomogeneous Influx: Dynamic Transitions