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arXiv 2610.16752cond-mat.mes-hall
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输运决定介观热力学中的谱距离

Transport Determines Spectral Distance in Mesoscopic Thermodynamics

Université libre de Bruxelles (ULB)(布鲁塞尔自由大学);International Solvay Institutes for Physics and Chemistry(国际索尔维物理化学研究所)

Giorgio Sonnino

AI总结:

该研究在介观正则模型中,从正埃尔米特输运张量推导热力学态间的谱距离,发现输运耦合决定度量各向异性,且无需独立度量或物理自旋变量。

摘要:

我们在介观正则模型中,从正埃尔米特输运张量推导热力学态之间的距离。演化生成元的精确一阶分解给出对易子范数和度量$G=2g^{-1}$,其中$g$为对称输运张量。反对称张量的梯度可改变演化,但不改变该距离。该构造允许依赖坐标的系数。对于恒定昂萨格系数,克利福德表示给出相同度量。在双通道热电系统中,归一化主距离的比值为$\frac{\text{sqrt}(1+ZT)+\text{sqrt}(ZT)}{1}$,输运耦合因此确定该度量的各向异性。该构造既不需要独立度量,也不需要物理自旋变量。

英文摘要:

We derive a distance between thermodynamic states from a positive Hermitian transport tensor within a mesoscopic canonical model. An exact first-order factorization of the evolution generator gives a commutator norm and the metric $G=2g$, where $g$ denotes the symmetric transport tensor. Gradients of the antisymmetric tensor can change the evolution, but they leave this distance unchanged. The construction allows coordinate-dependent coefficients. For constant Onsager coefficients, a Clifford representation gives the same metric. In a two-channel thermoelectric system, the ratio of normalized principal distances is $\sqrt{1+ZT}+\sqrt{ZT}$. Transport coupling thus fixes the anisotropy of this metric. The construction requires neither an independent metric nor a physical spin variable.

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

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