耗散稳态何时满足热力学占据定律
When dissipative steady states admit thermodynamic occupation laws
AI总结：
本文针对非平衡稳态中有限定常循环与全局精确速率比场的不相容问题，构建扇区分割几何结构，提出强偏置/快速重置、自主重分布等方法，获得热力学占据定律的适用条件，相关结果可应用于量子点激光器。
AI中文摘要：
非平衡稳态（NESS）通常缺乏热力学占据定律，因为对于同一马尔可夫生成元，有限的定常循环与全局精确的速率比场无法共存。本文构建了一种扇区分割几何结构，在不停止耗散的情况下克服了这种不相容性：熵产生的暴露与分离将产生熵的状态0排除在条件占据流形之外，同时保留其在耗散全图中；物理返回过程i→0→0*在强偏置/快速重置（SR）极限下成为有效马尔可夫过程。对于热力学完备的条件流形，自主重分布（AR）消除了残余无效循环，使速率比1-形式变得精确。热力学校准给出X_i=β(Δμ-ℱ_i^cost)和p_i=e^{X_i}/Z_𝒞，其中Z_𝒞=1+∑_i e^{X_i}；全图概率精确分解为P_α=(1-P_0)p_α。在SR极限下，动力学因子趋于1，而p_α→e^{X_α}/Z_𝒞，使得P_α→p_α，同时有限耗散持续存在。接近AR时，可积性在残余循环电流中线性丧失，而耗散则二次方开始。在二元零循环秩极限下，占据在维持Δμ偏置下自主重分布，产生反转费米-狄拉克定律，该定律应用于量子点激光器中的热展宽。该框架为耗散NESS中的热力学占据定律提供了构造性获取条件和失效诊断方法。
英文摘要：
Non-equilibrium steady states (NESSs) generally lack thermodynamic occupation laws because finite stationary circulation and a globally exact rate-ratio field cannot coexist for the same Markov generator. Here we construct a sector-separated geometry that overcomes this incompatibility without arresting dissipation. Entropy-production exposure-and-separation excludes the entropy-producing state~$0$ from the conditional occupation manifold while retaining it in the dissipative full graph; physical returns $i\to0\to0^\ast$ become effectively Markovian in the strong-bias/rapid-reset (SR) limit. For a thermodynamically complete conditional manifold, autonomous redistribution (AR) eliminates residual futile circulation, making the rate-ratio one-form exact. Thermodynamic calibration gives $X_i=β(Δμ- \mathcal F_i^{\mathrm{cost}})$ and $p_i=e^{X_i}/Z_\mathcal{C}$, with $Z_\mathcal{C}=1+\sum_i e^{X_i}$. Full-graph probabilities factorize exactly as $P_α=(1-P_0)p_α$. In the SR limit, the kinetic factor tends to unity while $p_α\to e^{X_α}/Z_\mathcal C$, yielding $P_α\to p_α$ while finite dissipation persists. Near AR, integrability is lost linearly in residual cycle current whereas dissipation begins quadratically. In the binary zero-cycle-rank limit, occupation redistributes autonomously under maintained $Δμ$ bias, yielding the inverted Fermi--Dirac law, which is applied to thermal smearing in quantum-dot lasers. The framework provides constructive acquisition conditions and failure diagnostics for thermodynamic occupation laws in dissipative NESSs.
