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Abstract：
Three approaches for determining the thermodynamic stability of irreversible processes are described in generalized formulations. The simplest is the Gibbs-Duhem theory, specialized to irreversible trajectories, which uses the concept of virtual displacement in the reverse direction. Its only drawback is that even a trajectory leading to an explosion is identified as a thermodynamically stable motion. In the second approach, we use a thermodynamic Lyapunov function and its time rate from the Lyapunov thermodynamic stability theory (LTS, previously known as CTTSIP). In doing so, we demonstrate that the second differential of entropy, a frequently used Lyapunov function, is useful only for investigating the stability of equilibrium states. Nonequilibrium steady states do not qualify. Without using explicit perturbation coordinates, we further identify asymptotic thermodynamic stability and thermodynamic stability under constantly acting disturbances of unperturbed trajectories as well as of nonequilibrium steady states. The third approach is also based on the Lyapunov function from LTS, but here we additionally use the rates of perturbation coordinates, based on the Gibbs relations and without using their explicit expressions, to identify not only asymptotic thermodynamic stability but also thermodynamic stability under constantly acting disturbances. Only those trajectories leading to an infinite rate of entropy production (unstable states) are excluded from this conclusion. Finally, we use these findings to formulate the Fourth Law of thermodynamics based on the thermodynamic stability. It is a comprehensive statement covering all nonequilibrium trajectories, close to as well as far from equilibrium. Unlike previous suggested \"fourth laws\", this one meets the same level of generality that is associated with the original zeroth to third laws. The above is illustrated using the Schlögl reaction with its multiple steady states in certain regions of operation.
摘要：
在广义公式中描述了三种确定不可逆过程热力学稳定性的方法。最简单的是Gibbs-Duhem理论,专门研究不可逆转的轨迹，它使用相反方向的虚拟位移的概念。其唯一的缺点是，甚至导致爆炸的轨迹也被认为是热力学稳定的运动。在第二种方法中，我们使用来自Lyapunov热力学稳定性理论的热力学Lyapunov函数及其时间速率(LTS，以前称为CTTSIP)。在这样做的时候，我们证明了熵的二阶微分，一个经常使用的Lyapunov函数，仅对研究平衡态的稳定性有用。非平衡稳态不合格。不使用明确的扰动坐标，我们进一步确定了渐近热力学稳定性和热力学稳定性，在不断作用的非扰动轨迹以及非平衡稳态的干扰下。第三种方法也基于LTS的Lyapunov函数，但是在这里我们还使用摄动坐标的速率，基于吉布斯关系，不使用它们的显式表达式，不仅要确定渐近的热力学稳定性，还要确定在不断作用的干扰下的热力学稳定性。只有那些导致熵产生率无限的轨迹（不稳定状态）被排除在这个结论之外。最后,我们利用这些发现来建立基于热力学稳定性的热力学第四定律。这是一份涵盖所有非平衡轨迹的全面声明，接近和远离平衡。与以前建议的“第四定律”不同，这一个符合与最初的第零到第三定律相关的一般性。使用在某些操作区域中具有多个稳态的Schl_gl反应来说明上文。
