论文标题
Lyapunov的功能，用于非平衡运输过程
Lyapunov function for non-equilibrium transport processes
论文作者
论文摘要
不可逆性是非平衡运输过程的关键特性。长期以来，人们坚持认为，熵的生产率是各种过程的Lyapunov函数，即最小熵产生的原理。但是，这样的原则是基于一些在实践中很少有效的强大假设。在这里，讨论了类似抛物线的运输过程的共同特征。然后提出一个定理，通量和相应力的点产物充当抛物面样运输过程的Lyapunov函数。这样的通量和力量是由它们的实际构型关系（例如傅立叶定律，给范围的法律等）来定义的。然后，分析了一些典型的运输过程。特别是对于热传导，理论和数值分析都表明，其lyapunov函数是进入的耗散，而是傅立叶定律有效的熵产生。目前的工作可能有助于进一步了解非平衡过程的不可逆性和数学解释。
Irreversibility is a critical property of non-equilibrium transport processes. An opinion has long been insisted that the entropy production rate is a Lyapunov function for all kinds of processes, that is, the principle of minimum entropy production. However, such principle is based on some strong assumptions that are rarely valid in practice. Here, the common features of parabolic-like transport processes are discussed. A theorem is then put forward that the dot products of fluxes and corresponding forces serve as Lyapunov function for parabolic-like transport processes. Such fluxes and forces are defined by their actual constitutive relations (e.g., the Fourier's law, the Fick's law, etc.). Then, some typical transport processes are analyzed. Particularly for heat conduction, both the theoretical and numerical analyses demonstrate that its Lyapunov function is the entransy dissipation rather that the entropy production, when the Fourier's law is valid. The present work could be helpful for further understanding on the irreversibility and the mathematical interpretation of non-equilibrium processes.
