Almost a century ago Onsager found a universal feature of all dissipative systems describing approach to thermodynamic equilibrium, the reciprocal relations. They hold for linear differential equations describing an evolution of macrovariables in vicinity of equilibrium states. It was assumed implicitly that underlying microdynamics is Hamiltonian and ergodic. The reversibility of Hamiltonian equations was one of the key features of microdynamics yielding Onsager’s relations. There are many situations where macrovariables, which are the slow parameters of microdynamics, describe, in fact, the mesoscopic phenomena. Thus, an additional course graining is to be done to get the equations of macroscopic theory. In particular, such are the problems of dislocation-mediated plasticity, where elimination of atomic degrees of freedom yields dislocation dynamics, and an additional averaging is needed to obtain the equations of macroscopic plasticity. This averaging problem is qualitatively different from the classical problems of nonequilibrium thermodynamics because the equations to be averaged are neither Hamiltonian nor ergodic, they are dissipative and irreversible. Besides, in driven systems there might be no equilibrium states. However, the basic question remains the same: Are there universal relations which the averaged equations must respect? In this paper, a positive answer to this question is given: the dependence of rates on forces must be potential in the limit of small and large forces. For small forces, this yields the relations which look quite similar to Onsager’s relations, though their origin caused by dissipative irreversible dynamics is quite different. In the limit of small forces a variational principle for dissipative potential is obtained; it reveals quite non-trivial reciprocities of macroscopic interactions. An immediate consequence of these results is the potentiality of the strain rate-stress constitutive relations in dislocation-mediated plasticity for small and large stresses. The reciprocity relations are illustrated by dislocation double-slip of a single crystal.

大约一个世纪前，Onsager发现了所有耗散系统的普遍特征，这些系统描述了热力学平衡的方法，即相互关系。它们适用于描述平衡变量附近宏观变量演化的线性微分方程。隐含地假设潜在的微观动力学是哈密顿量和遍历。哈密​​顿方程的可逆性是微动力学产生Onsager关系的关键特征之一。实际上，在许多情况下，作为微动力学的慢参数的宏变量描述了介观现象。因此，需要进行额外的过程粗化以得到宏观理论的方程。特别是位错介导的可塑性问题，其中消除原子的自由度会产生位错动力学，并且需要进行额外的平均以获得宏观可塑性方程。该平均问题在质量上与非平衡热力学的经典问题在质量上有所不同，因为要平均的方程既不是哈密顿方程也不是遍历方程，它们是耗散且不可逆的。此外，在驱动系统中可能没有平衡状态。但是，基本问题仍然是相同的：平均方程是否必须遵守普遍关系？在本文中，对这个问题给出了肯定的答案：费率对部队的依赖性必须在大小部队的限制范围内是潜在的。对于小型部队，这产生的关系看上去与翁萨格的关系非常相似，尽管它们的耗散不可逆动力学引起的起源是完全不同的。在小力的限制下，获得了耗散势的变分原理。它揭示了宏观互动的非常平凡的互惠。这些结果的直接结果是应变率-应力本构关系在小应力和大应力下在位错介导的可塑性中的潜力。互易关系用单晶的位错双滑移表示。这些结果的直接结果是应变率-应力本构关系在小应力和大应力下在位错介导的可塑性中的潜力。互易关系用单晶的位错双滑移表示。这些结果的直接结果是应变率-应力本构关系在小应力和大应力下在位错介导的可塑性中的潜力。互易关系用单晶的位错双滑移表示。