主动式热机的优化
Optimisation of an active heat engine
摘要：
在微尺度上优化热机在生物和人工纳米技术中有应用，并刺激非平衡统计物理学的理论研究。在这里，我们考虑非相互作用的过阻尼粒子所限制的外部谐波势，接触热库或随机自推进力（主动Ornstein-Uhlenbeck模型）。一个周期性的机器是由电势和噪声参数的周期性变化产生的。被动和主动模型之间的精确映射允许我们定义有效温度$T_{eff}(t)$，这对发动机的热力学性能是有意义的。我们表明，$T_{eff}(t)$是不同的，从所有其他已知的活动温度，通常用于静态的情况下。该映射允许我们优化主动发动机，无论持续时间或自推进速度的值如何。特别是-通过线性不可逆热力学（小振幅的周期）-我们给出了明确的公式，最佳周期和相位延迟（两个调制参数，刚度和温度之间）实现最大功率与Curzon-Ahlborn效率。在准静态极限下，$T_{eff}(t)$的公式简化并与最近提出的随机热力学温度相吻合，具有最大效率的紧凑表达式。在最近的文献中被忽视的一点是，在没有一致的有效温度定义的情况下，定义效率是困难的。
英文摘要：
Optimisation of heat engines at the micro-scale has applications in biological and artificial nano-technology, and stimulates theoretical research in non-equilibrium statistical physics. Here we consider non-interacting overdamped particles confined by an external harmonic potential, in contact either with a thermal reservoir or with a stochastic self-propulsion force (active Ornstein-Uhlenbeck model). A cyclical machine is produced by periodic variation of the parameters of the potential and of the noise. An exact mapping between the passive and the active model allows us to define the effective temperature $T_{eff}(t)$ which is meaningful for the thermodynamic performance of the engine. We show that $T_{eff}(t)$ is different from all other known active temperatures, typically used in static situations. The mapping allows us to optimise the active engine, whatever are the values of the persistence time or self-propulsion velocity. In particular - through linear irreversible thermodynamics (small amplitude of the cycle) - we give explicit formula for the optimal cycle period and phase delay (between the two modulated parameters, stiffness and temperature) achieving maximum power with Curzon-Ahlborn efficiency. In the quasi-static limit, the formula for $T_{eff}(t)$ simplifies and coincides with a recently proposed temperature for stochastic thermodynamics, bearing a compact expression for the maximum efficiency. A point - overlooked in recent literature - is made about the difficulty in defining efficiency without a consistent definition of effective temperature.
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