We consider the non-equilibrium steady state induced by two infinitely extended quantum thermal reservoirs at different inverse temperatures β + Δβ, β − Δβ and derive a work relation. We consider global cyclic operations and derive an upper bound of the work density in one-dimensional quantum lattice systems. This relation reproduces the second law of thermodynamics in the equilibrium limit Δβ → 0. A free fermion system is discussed as an example, and the physical interpretation is given to the upper bound.

中文翻译：

---

一维量子晶格系统在非平衡稳态下的功关系

我们考虑在不同的温度下反诱导由两个无限扩展的量子热水库非平衡稳态β +Δ β，β - Δ β和导出工作关系。我们考虑全局循环操作，并推导一维量子晶格系统中的工作密度上限。这种关系再现Δ在平衡热力学限制的第二定律β →交通0。自由费米系统为例进行讨论，并且将物理解释是考虑到上限。