Onsager fluxes proposed by D.G.B. Edelen assume that the same symmetry, nonlinear Onsager reciprocal relations, holds near and far from equilibrium. This assumption leads to exact differential 1-form J ⋅ dX everywhere, where J and X are thermodynamic fluxes and forces, respectively. However, thermodynamic fluxes far from equilibrium are characterized by symmetry breaking, which lead to the inexact differential 1-form. It is shown in this paper that the inexact differential 1-form J ⋅ dX should be represented by multiple independent scalar-valued functions. Generalized Onsager fluxes are obtained based on such representation. Generalized Onsager fluxes do not satisfy the nonlinear Onsager reciprocal relations and contain multiple independent scalar-valued functions, so they are suitable to thermodynamic fluxes far from equilibrium. Generalized Onsager fluxes embody Onsager fluxes as a special case. Therefore, generalized Onsager fluxes provide a unified framework for thermodynamic fluxes near and far from equilibrium.

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基于不精确微分 1-形式的广义 Onsager 通量

DGB Edelen 提出的 Onsager 通量假设相同的对称性、非线性 Onsager 互反关系在接近和远离平衡点时保持不变。这个假设导致精确微分 1-形式 J ⋅ dX 到处，其中 J 和 X 分别是热力学通量和力。然而，远离平衡的热力学通量具有对称性破缺的特征，这会导致不精确的微分 1-形式。本文表明，不精确微分 1-形式 J ⋅ dX 应由多个独立的标量值函数表示。基于这种表示获得广义 Onsager 通量。广义昂萨格通量不满足非线性昂萨格倒数关系，包含多个独立的标量值函数，适用于远离平衡态的热力学通量。通用的 Onsager 通量体现了 Onsager 通量作为一个特例。因此，广义 Onsager 通量为接近和远离平衡的热力学通量提供了一个统一的框架。