远非平衡态热力学的最陡熵升模型最大熵产生原理的统一实现
Steepest Entropy Ascent Model for Far-Non-Equilibrium Thermodynamics. Unified Implementation of the Maximum Entropy Production Principle
摘要：
通过适当的重新表述，我们将几种著名的描述非平衡态动力学的不同方法的数学框架转换成一个统一的表述，将作者在量子热力学的前期工作中引入的最陡熵上升（SEA）动力学的概念扩展到这样的框架中。本公式也构成了量子热力学框架的推广。在SEA建模原理中，几何度量起着关键作用，相对于几何度量来测量状态空间中的轨迹的长度。在接近平衡极限时，度规张量与Onsager广义电阻率张量有关。因此，通过确定一个合适的度规场，它将Onsager广义电阻推广到任意远的非平衡域，大多数现有的非平衡热力学理论可以这样一种方式铸造，即状态表现出自发的趋势，沿着与守恒约束和边界条件相容的SEA路径在状态空间中演化。由此产生的统一家庭的SEA动力学模型是内在的和强烈一致的热力学第二定律。熵产生的非负性是SEA动力学的一个易于证明的一般特征。在几个不同的方法来非平衡描述，我们认为在这里，SEA的概念还没有被调查过。我们相信它定义了所谓的最大熵产生原理的确切含义和一般有效性的领域。希望本统一的方法可以证明是有用的，提供一个新的基础，有效的，一致的，数值模型和理论处理的不可逆的保守松弛到平衡从远非平衡态。
英文摘要：
By suitable reformulations, we cast the mathematical frameworks of several well-known different approaches to the description of non-equilibrium dynamics into a unified formulation, which extends to such frameworks the concept of Steepest Entropy Ascent (SEA) dynamics introduced by the present author in previous works on quantum thermodynamics. The present formulation constitutes a generalization also for the quantum thermodynamics framework. In the SEA modeling principle a key role is played by the geometrical metric with respect to which to measure the length of a trajectory in state space. In the near equilibrium limit, the metric tensor is related to the Onsager's generalized resistivity tensor. Therefore, through the identification of a suitable metric field which generalizes the Onsager generalized resistance to the arbitrarily far non-equilibrium domain, most of the existing theories of non-equilibrium thermodynamics can be cast in such a way that the state exhibits a spontaneous tendency to evolve in state space along the path of SEA compatible with the conservation constraints and the boundary conditions. The resulting unified family of SEA dynamical models is intrinsically and strongly consistent with the second law of thermodynamics. Non-negativity of the entropy production is a readily proved general feature of SEA dynamics. In several of the different approaches to non-equilibrium description we consider here, the SEA concept has not been investigated before. We believe it defines the precise meaning and the domain of general validity of the so-called Maximum Entropy Production Principle. It is hoped that the present unifying approach may prove useful in providing a fresh basis for effective, thermodynamically consistent, numerical models and theoretical treatments of irreversible conservative relaxation towards equilibrium from far non-equilibrium states.
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