发表机构
West Los Angeles College（西洛杉矶学院）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文针对布朗热机构建逆设计问题，推导了任意温度场的稳态电流与概率密度，得到准静态效率最优解及有限电流下的优化条件，明确了最大化电流的能垒平衡关系。
AI 中文摘要
布朗热机中的空间温度场通常是预先给定的，随后再计算由此产生的输运性质和热力学性质。本文构建了互补的逆设计问题：确定温度分布和能垒高度以优化选定的热力学目标。我们考虑在恒定反向负载下，处于对称三角周期势中的过阻尼布朗粒子，推导了任意有界温度场（满足 $T_c\le T(x)\le T_h$）的精确稳态电流和概率密度。在准静态极限下，效率成为上坡和下坡分支上两个逆温度积分的精确泛函。在逐点温度约束下，其严格的全局最大值为 $\eta_{\max}=1-T_c/T_h$，除测度为零的集合外，唯一由“上坡热、下坡冷”的分段常数分布实现。然而在有限电流下，优化会发生定性变化，因为电流由循环亲和力和非局部输运电阻共同决定。我们推导了精确的泛函梯度和对应的箱约束最优性条件，表明最大化电流或功率的分布通常与准静态效率最优解不同。对于任意给定的温度场，最大化电流的能垒在热整流的边际增益与输运电阻的边际增加之间满足精确平衡，特征估计为 $U_0^*\simeq T_{\rm act}$，其中 $T_{\rm act}^{-1}=(2/L)\int_0^{L/2}\dd x/T(x)$。
英文摘要
Spatial temperature fields in Brownian heat engines are commonly prescribed \emph{a priori}, and the resulting transport and thermodynamic properties are then calculated. Here we formulate the complementary inverse-design problem: determining the temperature profile and barrier height that optimize a chosen thermodynamic objective. We consider an overdamped Brownian particle in a symmetric triangular periodic potential under a constant opposing load and derive the exact stationary current and probability density for an arbitrary bounded temperature field, $\Tc\le T(x)\le\Th$. In the quasistatic limit, the efficiency becomes an exact functional of two inverse-temperature integrals over the uphill and downhill branches. Its rigorous global maximum under the pointwise temperature bounds is $η_{\max}=1-\Tc/\Th$, attained uniquely, up to sets of measure zero, by the hot-uphill/cold-downhill piecewise-constant profile. At finite current, however, the optimization changes qualitatively because the current is determined jointly by the cycle affinity and a nonlocal transport resistance. We derive the exact functional gradient and the corresponding box-constrained optimality conditions, showing that the current- or power-maximizing profile generally differs from the quasistatic efficiency optimum. For any prescribed temperature field, the current-maximizing barrier satisfies an exact balance between the marginal gain in thermal rectification and the marginal increase in transport resistance, with the characteristic estimate $U_0^*\simeq T_{\rm act}$, where $T_{\rm act}^{-1}=(2/L)\int_0^{L/2}\dd x/T(x)$.
