This work proposes a novel approach for the study of open systems described by completely irreversible reaction mechanisms in non-homogeneous systems and subject to non-equilibrium boundary conditions. Using the non-equilibrium thermodynamics framework, we consider that in an autonomous system of reaction–diffusion equations, the thermodynamic potentials can be constructed from a Lyapunov function that depends directly on the eigenvalues and eigenvectors of the linearized problem. By interpreting this Lyapunov function as the free energy and redefining the chemical potentials, we were able to demonstrate the local stability properties of non-equilibrium stationary states, i. e., states that do not change with time due to a complex equilibration of internal and external flows. We demonstrate the consistency of our hypotheses with basic thermodynamic principles such as the spectral decomposition of entropy production and the Glansdorff–Prigogine evolution criterion. We discuss how our approach allows us to understand thermodynamic systems without assuming equilibrium or any kind of reversibility.

中文翻译：

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渐近稳定的开放和不可逆化学反应扩散系统中的能量和熵

这项工作提出了一种研究开放系统的新方法，该系统由非均质系统中完全不可逆的反应机制描述，并受非平衡边界条件的约束。使用非平衡热力学框架，我们认为在反应扩散方程的自治系统中，热力学势可以由直接依赖于线性化问题的特征值和特征向量的 Lyapunov 函数构建。通过将这个 Lyapunov 函数解释为自由能并重新定义化学势，我们能够证明非平衡稳态的局部稳定性特性，IE，由于内部和外部流动的复杂平衡，不随时间变化的状态。我们证明了我们的假设与基本热力学原理的一致性，例如熵产生的光谱分解和 Glansdorff-Prigogine 演化准则。我们讨论了我们的方法如何让我们在不假设平衡或任何可逆性的情况下理解热力学系统。