Biswas Tanmoy, Junior A de Oliveira, Horodecki Michał, Korzekwa Kamil
International Centre for Theory of Quantum Technologies, University of Gdańsk, Wita Stwosza 63, 80-308 Gdańsk, Poland.
Faculty of Physics, Astronomy and Applied Computer Science, Jagiellonian University, 30-348 Kraków, Poland.
Phys Rev E. 2022 May;105(5-1):054127. doi: 10.1103/PhysRevE.105.054127.
The fluctuation-dissipation theorem is a fundamental result in statistical physics that establishes a connection between the response of a system subject to a perturbation and the fluctuations associated with observables in equilibrium. Here we derive its version within a resource-theoretic framework, where one investigates optimal quantum state transitions under thermodynamic constraints. More precisely, we first characterize optimal thermodynamic distillation processes, and then we prove a relation between the amount of free energy dissipated in such processes and the free-energy fluctuations of the initial state of the system. Our results apply to initial states given by either asymptotically many identical pure systems or an arbitrary number of independent energy-incoherent systems, and they allow not only for a state transformation but also for the change of Hamiltonian. The fluctuation-dissipation relations we derive enable us to find the optimal performance of thermodynamic protocols such as work extraction, information erasure, and thermodynamically free communication, up to second-order asymptotics in the number N of processed systems. We thus provide a first rigorous analysis of these thermodynamic protocols for quantum states with coherence between different energy eigenstates in the intermediate regime of large but finite N.
涨落耗散定理是统计物理学中的一个基本结果，它建立了一个受到微扰的系统的响应与平衡态下可观测量相关涨落之间的联系。在此，我们在资源理论框架内推导其版本，其中人们研究热力学约束下的最优量子态跃迁。更确切地说，我们首先刻画最优热力学蒸馏过程，然后证明在此类过程中耗散的自由能数量与系统初始态的自由能涨落之间的关系。我们的结果适用于由渐近多个相同纯系统或任意数量独立能量非相干系统给出的初始态，并且它们不仅允许态变换，还允许哈密顿量的变化。我们推导的涨落耗散关系使我们能够找到诸如功提取、信息擦除和热力学自由通信等热力学协议的最优性能，直至处理系统数量(N)的二阶渐近情况。因此，我们首次对大但有限的(N)的中间区域中不同能量本征态之间具有相干性的量子态的这些热力学协议进行了严格分析。
