论文标题
不确定随机过程的非平衡热力学
Nonequilibrium thermodynamics of uncertain stochastic processes
论文作者
论文摘要
随机热力学是在所有热力学参数完美知识的假设下制定的。但是，在任何实际实验中，关于温度，化学势，能量光谱等的精确值的不确定性都存在非零的不确定性。在这里，我们研究了这种不确定性如何改变随机热力学的理论。我们考虑两种情况：在（称为\ emph {效率}）方案中，我们修复了（未知，随机生成的）实验设备，然后反复观察该系统的（随机）轨迹（随机）轨迹。相反，在（称为\ emph {现象学}）方案中，（未知）设备为每个轨迹重新生成。在两种情况下，我们都会得出热力学量的表达式。我们还讨论了有效（场景）熵产生（EP）的物理解释，得出有效的不匹配成本，并对实现量子点的有效热力学进行了数值分析，该量子点实现了以不确定的温度实现位擦除的量子点。然后，我们分析了两个状态分布之间移动的协议，以最大程度地提取有效的工作提取。接下来，我们研究信息的有效热力学价值，重点是系统初始化和协议开始之间存在延迟的情况。最后，我们为现象学EP得出了详细的和综合的波动定理（FTS）。特别是，我们展示了现象学FTS如何解释轨迹运行越长的事实，其提供的信息越多，与精确的实验设备相关的信息越多，因此其产生的EP越少。
Stochastic thermodynamics is formulated under the assumption of perfect knowledge of all thermodynamic parameters. However, in any real-world experiment, there is non-zero uncertainty about the precise value of temperatures, chemical potentials, energy spectrum, etc. Here we investigate how this uncertainty modifies the theorems of stochastic thermodynamics. We consider two scenarios: in the (called \emph{effective}) scenario we fix the (unknown, randomly generated) experimental apparatus and then repeatedly observe (stochastic) trajectories of the system for that fixed apparatus. In contrast, in a (called \emph{phenomenological}) scenario the (unknown) apparatus is re-generated for each trajectory. We derive expressions for thermodynamic quantities in both scenarios. We also discuss the physical interpretation of effective (scenario) entropy production (EP), derive the effective mismatch cost, and provide a numerical analysis of the effective thermodynamics of a quantum dot implementing bit erasure with uncertain temperature. We then analyze the protocol for moving between two state distributions that maximize effective work extraction. Next, we investigate the effective thermodynamic value of information, focusing on the case where there is a delay between the initialization of the system and the start of the protocol. Finally, we derive the detailed and integrated fluctuation theorems (FTs) for the phenomenological EP. In particular, we show how the phenomenological FTs account for the fact that the longer a trajectory runs, the more information it provides concerning the precise experimental apparatus, and therefore the less EP it generates.
