In this paper we study the nonequilibrium evolution of a quantum Brownian oscillator, modeling the internal degree of freedom of a harmonic atom or an Unruh–DeWitt detector, coupled to a nonequilibrium and nonstationary quantum field bath and inquire whether a fluctuation–dissipation relation (FDR) can exist after/if it approaches equilibration. This is a nontrivial issue because a squeezed field bath cannot reach equilibration and yet, as this work shows, the system oscillator indeed can, which is a necessary condition for FDRs. We discuss three different settings: (A) The bath field essentially remains in a squeezed thermal state throughout, whose squeeze parameter is a mode- and time-independent constant. This situation is often encountered in quantum optics and quantum thermodynamics. (B) The bath field is initially in a thermal state, but is subjected to a parametric process leading to mode- and time-dependent squeezing. This scenario is encountered in cosmology and dynamical Casimir effects. The squeezing in the bath in both types of processes will affect the oscillator’s nonequilibrium evolution. We show that at late times it approaches equilibration and this stationarity condition warrants the existence of a FDR. The trait of squeezing is marked by the oscillator’s effective equilibrium temperature, and the proportionality factor in the FDR is only related to the stationary component of the noise kernel of the bath field. Setting (C) is more subtle: A finite system–bath coupling strength can set the oscillator in a squeezed state even though the bath field is stationary and does not engage in any parametric process. The squeezing of the system in this case is in general time-dependent but becomes constant when the internal dynamics is fully relaxed. We begin with comments on the broad range of physical processes involving squeezed thermal baths and end with some remarks on the significance of FDRs in capturing the essence of quantum backreaction in nonequilibrium and stochastic systems.

在本文中，我们研究了量子布朗振荡器的非平衡演化，模拟谐波原子或 Unruh-DeWitt 探测器的内部自由度，耦合到非平衡和非平稳量子场浴，并询问是否存在涨落-耗散关系 (FDR) ) 可以在/如果它接近平衡后存在。这是一个重要的问题，因为挤压场浴不能达到平衡，然而，正如这项工作所示，系统振荡器确实可以，这是 FDR 的必要条件。我们讨论了三种不同的设置：（A）浴场基本上始终处于挤压热状态，其挤压参数是与模式和时间无关的常数。这种情况在量子光学和量子热力学中经常遇到。(B) 浴场最初处于热状态，但受到参数过程的影响，导致模式和时间相关的挤压。在宇宙学和动力学卡西米尔效应中会遇到这种情况。在两种类型的过程中在浴中的挤压都会影响振荡器的非平衡演化。我们表明，在后期它接近平衡并且这种平稳条件保证了 FDR 的存在。挤压特性以振荡器的有效平衡温度为标志，FDR中的比例因子仅与浴场噪声核的平稳分量有关。设置 (C) 更加微妙：即使浴场是静止的并且不参与任何参数化过程，有限的系统-浴耦合强度也可以将振荡器设置为挤压状态。在这种情况下，系统的挤压通常与时间有关，但当内部动力学完全放松时会变得恒定。我们首先评论涉及挤压热浴的广泛物理过程，最后评论 FDR 在捕捉非平衡和随机系统中的量子逆反应本质方面的重要性。