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Path Between Thermodynamics States01:21

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Consider the two thermodynamic processes involving an ideal gas that are represented by paths AC and ABC in Figure 1:
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Consistent with the law of mass action, an equilibrium stressed by a change in concentration will shift to re-establish equilibrium without any change in the value of the equilibrium constant, K. When an equilibrium shifts in response to a temperature change, however, it is re-established with a different relative composition that exhibits a different value for the equilibrium constant.
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Pattern formation revisited within nonequilibrium thermodynamics: Burgers'-type equation.

Václav Klika1

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|November 10, 2021
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Summary

This study explores reaction-diffusion systems using nonequilibrium thermodynamics. A new term from diffusion kinetic energy drives reactions, potentially creating non-periodic patterns and enriching classical models.

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Area of Science:

  • Physical Chemistry
  • Nonlinear Dynamics
  • Thermodynamics

Background:

  • Reaction-diffusion systems are fundamental in various scientific fields.
  • Non-equilibrium thermodynamics provides a framework for analyzing these systems.
  • A nonstandard entropy balance splitting reveals new insights.

Purpose of the Study:

  • To investigate the impact of a diffusion kinetic energy term on reaction-diffusion phenomena.
  • To derive and analyze governing equations within a modified thermodynamic framework.
  • To explore pattern formation and stability in reaction-diffusion systems.

Main Methods:

  • Utilizing a nonstandard splitting of the entropy balance.
  • Applying standard constitutive relations from linear non-equilibrium thermodynamics.
  • Deriving governing equations for a two-species reaction-diffusion system.
  • Analyzing the connection to Burgers' equation with a source term.

Main Results:

  • A new thermodynamic force derived from diffusion kinetic energy drives reaction kinetics.
  • Governing equations are linked to Burgers' equation, allowing for non-periodic pattern emergence.
  • Transients resembling saw-tooth solutions to Burgers' equation are predicted.
  • Turing's reaction-diffusion model shows robustness to this new term when small.

Conclusions:

  • The inclusion of diffusion kinetic energy can lead to richer pattern formation in reaction-diffusion systems.
  • Non-standard reaction kinetics, beyond the law of mass action, can significantly alter system behavior.
  • This approach offers a pathway to explore novel phenomena in classical reaction-diffusion models.