The treatment of quantum thermodynamic systems beyond weak coupling is of increasing relevance, yet extremely challenging. The evaluation of thermodynamic quantities in strong-coupling regimes requires a nonperturbative knowledge of the bath dynamics, which in turn relies on heavy numerical simulations. To tame these difficulties, considering thermal bosonic baths linearly coupled to the open system, we derive expressions for heat, work, and average system-bath interaction energy that only involve the autocorrelation function of the bath and two-time expectation values of system operators. We then exploit the pseudomode approach, which replaces the physical continuous bosonic bath with a small finite number of damped, possibly interacting, modes, to numerically evaluate these relevant thermodynamic quantities. We show in particular that this method allows for an efficient numerical evaluation of thermodynamic quantities in terms of one-time expectation values of the open system and the pseudomodes. We apply this framework to the investigation of two paradigmatic situations. In the first instance, we study the entropy production for a two-level system (TLS) coupled to an ohmic bath, simulated via interacting pseudomodes, allowing for the presence of time-dependent driving. Secondly, we consider a quantum thermal machine composed of a TLS interacting with two thermal baths at different temperatures, showing that an appropriate sinusoidal modulation of the coupling with the cold bath only is enough to obtain work extraction.

中文翻译：

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强耦合量子热力学的伪模处理


超越弱耦合的量子热力学系统的处理越来越重要，但也极具挑战性。在强耦合状态下评估热力学量需要对浴动力学有非扰动知识，而这反过来又依赖于大量的数值模拟。为了解决这些困难，考虑到与开放系统线性耦合的热玻色子浴，我们推导出了热、功和平均系统-浴相互作用能的表达式，这些表达式仅涉及浴的自相关函数和系统操作员的两倍期望值。然后，我们利用伪模方法，用少量有限数量的阻尼（可能是相互作用的）模式代替物理连续玻色子浴，以数值计算这些相关的热力学量。我们特别表明，这种方法允许根据开放系统和伪模的一次性期望值对热力学量进行有效的数值评估。我们将这个框架应用于两种范式情况的研究。首先，我们研究了与欧姆浴耦合的两能级系统 （TLS） 的熵产生，通过相互作用的伪模进行模拟，允许存在瞬态驾驶。其次，我们考虑了一个由 TLS 组成的量子热机与不同温度下的两个热浴相互作用，表明仅与冷浴耦合的适当正弦调制就足以获得功提取。