各向异性涨落能量收集的精细化界
Refined bounds on energy harvesting from anisotropic fluctuations
AI总结：
针对两自由度过阻尼布朗粒子热各向异性能量收集问题，移除熵恒定假设，证明可通过倾斜热力学循环降低耗散，且最优循环可由倾斜低维子空间等周问题解局部近似。
摘要：
我们研究具有两个自由度（DoF）的过阻尼布朗粒子，它们被限制在随时间变化的二次势阱中，且各自的自由度同时与不同温度的热浴接触。热涨落的各向异性可通过适当调控约束势来提取功。近期研究提出了可提取最大功的问题，并在粒子分布熵（热力学态）在整个热力学循环中保持恒定的简化假设下进行了计算。事实上，已有研究表明，可提取的最大功等价于求解一个等周问题：热力学态经历的2-Wasserstein长度量化了耗散，而该耗散可与量化热各向异性提取功的面积积分进行权衡。本文中，我们移除了熵恒定的简化假设。我们证明，提取功的计算方式与熵保持恒定的情况类似，而通过在增加一个维度的热力学空间中适当倾斜热力学循环，可以降低耗散。最优循环可通过倾斜低维子空间中等周问题的解进行局部近似。
英文摘要：
We consider overdamped Brownian particles with two degrees of freedom (DoF) that are confined in a time-varying quadratic potential and are in simultaneous contact with heat baths of different temperatures along the respective DoF. The anisotropy in thermal fluctuations can be used to extract work by suitably manipulating the confining potential. The question of what the maximal amount of work that can be extracted is has been raised in recent work, and has been computed under the simplifying assumption that the entropy of the distribution of particles (thermodynamic states) remains constant throughout a thermodynamic cycle. Indeed, it was shown that the maximal amount of work that can be extracted amounts to solving an isoperimetric problem, where the 2-Wasserstein length traversed by thermodynamic states quantifies dissipation that can be traded off against an area integral that quantifies work drawn out of the thermal anisotropy. Here, we remove the simplifying assumption on constancy of entropy. We show that the work drawn can be computed similarly to the case where the entropy is kept constant while the dissipation can be reduced by suitably tilting the thermodynamic cycle in a thermodynamic space with one additional dimension. Optimal cycles can be locally approximated by solutions to an isoperimetric problem in a tilted lower-dimensional subspace.
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