Extremal principles can generally be divided into two rather distinct classes. There are, on the one hand side, formulations based on the Lagrangian or Hamiltonian mechanics, respectively, dealing with time dependent problems, but essentially resting on conservation of energy and thus being not applicable to dissipative systems in a consistent way. On the other hand, there are formulations based essentially on maximizing the dissipation, working efficiently for the description of dissipative systems, but being not suitable for including inertia effects. Many at-tempts can be found in the literature to overcome this split into incompatible principles. How-ever, essentially all of them possess an unnatural appearance. In this work, we suggest a solution to this dilemma resting on an additional assumption based on the thermodynamic driving forces involved. Applications to a simple dissipative structure and a material with varying mass demonstrate the capability of the proposed approach.

翻译：极值原理通常可分为两种截然不同的类型。一方面，基于拉格朗日力学或哈密顿力学的公式适用于时间依赖性问题，但这些公式本质上依赖于能量守恒，因此无法以一致的方式应用于耗散系统。另一方面，基于最大化耗散的公式虽能有效描述耗散系统，但无法包含惯性效应。文献中虽有众多尝试试图解决这两种互斥原理之间的分裂，但本质上所有方法均存在不自然之处。本文基于所涉及的热力学驱动力提出一种额外假设，为该困境提供解决方案。通过对简单耗散结构及变质量材料的应用实例，验证了所提出方法的可行性。