The Onsager reciprocity relations were formulated in the context of irreversible thermodynamics, but they are based on assumptions that have a wider applicability. Here, we present simulations testing the Onsager relations between surface-coupled diffusive and bulk fluxes in a system prepared in a nonequilibrium steady state. The system consists of a mixture of two identical species maintained at different temperatures inside a channel. In order to tune the friction of the two species with the walls independently, while keeping the particle-wall interaction potentials the same, we allow the kinematics of particle-wall collisions to be different: “bounce-back” ($B$) or “specular” ($S$). In the $BB$ case, diffusio-capillary transport can only take place if the two species have different temperatures. We find that the Onsager reciprocity relations are obeyed in the linear regime, even in the $BB$ case where all fluxes are the result of perturbing the system from a nonequilibrium steady state in a way that does not satisfy time-reversal symmetry. Our Letter provides a direct, numerical illustration of the validity of the Onsager relations outside their original range of application, and suggests their relevance for transport in driven or active systems.

中文翻译：

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驱动系统中 Onsager 关系的数值测试

Onsager 互易关系是在不可逆热力学的背景下制定的，但它们基于具有更广泛适用性的假设。在这里，我们提出模拟测试在非平衡稳态下制备的系统中表面耦合扩散通量和体积通量之间的 Onsager 关系。该系统由在通道内保持在不同温度下的两种相同物种的混合物组成。为了独立调整两种物质与壁的摩擦，同时保持粒子-壁相互作用势相同，我们允许粒子-壁碰撞的运动学不同：“反弹”（$乙$) 或“镜面反射” ($\mathrm{小号}$). 在里面$乙乙$在这种情况下，扩散毛细管传输只有在两种物质具有不同温度的情况下才能发生。我们发现 Onsager 互易关系在线性状态下得到遵守，即使在$乙乙$所有通量都是以不满足时间反演对称性的方式从非平衡稳态扰动系统的结果。我们的信提供了 Onsager 关系在其原始应用范围之外的有效性的直接数字说明，并表明它们与驱动或主动系统中的传输相关。