We establish a connection between non-Markovianity and negative entropy production rate for various classes of quantum operations. We analyse several aspects of unital and thermal operations in connection with resource theories of purity and thermodynamics. We fully characterize Lindblad operators corresponding to unital operations. We also characterize the Lindblad dynamics for a large class of thermal operations. We next generalize the definition of the entropy production rate for the non-equilibrium case to connect it with the rate of change of free energy of the system, and establish complementary relations between non-Markovianity and maximum loss of free energy. We naturally conclude that non-Markovianity in terms of divisibility breaking is a necessary resource for the backflow of other resources like purity or free energy under the corresponding allowed operations.

中文翻译：

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资源互转换视角下的非马尔可夫热力学效用

我们为各种类型的量子运算建立了非马尔可夫性和负熵生产率之间的联系。我们结合纯度和热力学资源理论分析了单元和热操作的几个方面。我们充分描述了对应于单元运算的Lindblad运算符的特征。我们还为大型热操作表征了Lindblad动力学。接下来，我们将广义不平衡情况下熵产生率的定义与系统自由能的变化率联系起来，并建立非马尔可夫性与最大自由能损失之间的互补关系。