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arXiv 2108.05937quant-phcond-mat.stat-mech
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任意Lindblad主方程的量子涨落定理

A quantum fluctuation theorem for any Lindblad master equation

Gabriele De Chiara, Alberto Imparato

备注：
Accepted version
发表信息：
Phys. Rev. Res. 4, 023230 (2022)
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摘要：

我们提出了一个一般的量子涨落定理的熵产生的开放量子系统耦合到多个环境，不一定在平衡。这样的一般定理，当限制到弱耦合和马尔可夫制度，本地和全球的主方程，证实了本地量子主方程的热力学一致性。该定理是真正的量子，因为它可以用厄米算符的守恒来表示，描述系统状态算符的动力学和浴中熵的变化。积分涨落定理是由这样一个算子的性质得出的。此外，当系统由含时哈密顿量描述时，它也是有效的。因此，量子Jarzynski等式是这里给出的一般结果的一个特例。此外，我们的结果可以扩展到非热浴，只要保持微可逆性。我们提出了一些数值例子来展示以前获得的确切结果。最后，我们推广的涨落定理的情况下，系统和浴之间的相互作用是明确考虑。我们表明，涨落定理相当于全球密度矩阵的时间反演动力学和两个时间的关联函数沿涉及浴的熵单独的前向动力学之间的关系。

英文摘要：

We present a general quantum fluctuation theorem for the entropy production of an open quantum system coupled to multiple environments, not necessarily at equilibrium. Such a general theorem, when restricted to the weak-coupling and Markovian regime, holds for both local and global master equations, corroborating the thermodynamic consistency of local quantum master equations. The theorem is genuinely quantum, as it can be expressed in terms of conservation of a Hermitian operator, describing the dynamics of the system state operator and of the entropy change in the baths. The integral fluctuation theorem follows from the properties of such an operator. Furthermore, it is also valid when the system is described by a time-dependent Hamiltonian. As such, the quantum Jarzynski equality is a particular case of the general result presented here. Moreover, our result can be extended to nonthermal baths, as long as microreversibility is preserved. We present some numerical examples to showcase the exact results previously obtained. We finally generalize the fluctuation theorem to the case where the interaction between the system and the bath is explicitly taken into account. We show that the fluctuation theorem amounts to a relation between time-reversed dynamics of the global density matrix and a two-time correlation function along the forward dynamics involving the baths' entropy alone.

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