We generalize an idea in the works of Landauer and Bennett on computations, and Hill’s in chemical kinetics, to emphasize the importance of kinetic cycles in mesoscopic nonequilibrium thermodynamics (NET). For continuous stochastic systems, a NET in phase space is formulated in terms of cycle affinity \(\nabla \wedge \big (\mathbf{D}^{-1}\mathbf{b}\big )\) and vorticity potential \(\mathbf{A}(\mathbf{x})\) of the stationary flux \(\mathbf{J}^{*}=\nabla \times \mathbf{A}\). Each bivectorial cycle couples two transport processes represented by vectors and gives rise to Onsager’s notion of reciprocality; the scalar product of the two bivectors \(\mathbf{A}\cdot \nabla \wedge \big (\mathbf{D}^{-1}\mathbf{b}\big )\) is the rate of local entropy production in the nonequilibrium steady state. An Onsager operator that relates vorticity to cycle affinity is introduced.

我们在Landauer和Bennett的工作中概括了一个思想，在化学动力学中概括了Hill的思想，以强调动力学循环在介观非平衡热力学（NET）中的重要性。对于连续随机系统，根据周期亲和力\（\ nabla \ wedge \ big（\ mathbf {D} ^ {-1} \ mathbf {b} \ big} \）和涡旋势\固定通量\（\ mathbf {J} ^ {*} = \ nabla \ times \ mathbf {A} \）的（\ mathbf {A}（\ mathbf {x}）\）。每个双矢量周期将两个由矢量表示的传输过程耦合在一起，并产生了昂萨格的互惠性概念。两个双向量的标量积\（\ mathbf {A} \ cdot \ nabla \ wedge \ big（\ mathbf {D} ^ {-1} \ mathbf {b} \ big} \）是非平衡稳态下局部熵产生的速率。介绍了将涡度与循环亲和力相关联的Onsager运算符。