远离平衡态的量子系统中的冷点：局部熵和绝对零度附近的温度
Cold spots in quantum systems far from equilibrium: local entropies and temperatures near absolute zero
摘要：
我们考虑一个由热力学第三定律激发的问题：在非平衡量子系统中，是否存在任意接近绝对零度的局部温度？我们考虑纳米级量子导体，其源极储存器保持在有限温度，漏极保持在或接近绝对零度，这是线性响应理论范围之外的问题。我们得到的本地温度接近绝对零度时，从有限的温度水库起源的电子进行破坏性的量子干涉。通过数值求解一个非线性方程组描述平衡的扫描热电探针与系统的局部温度计算，我们获得了很好的协议与分析结果使用索末菲展开。引入了非平衡态量子系统的局域熵，并将其作为偏离局域平衡态的度量。结果表明，当探针温度趋于零时，系统的局部熵趋于零，符合热力学第三定律。
英文摘要：
We consider a question motivated by the third law of thermodynamics: can there be a local temperature arbitrarily close to absolute zero in a nonequilibrium quantum system? We consider nanoscale quantum conductors with the source reservoir held at finite temperature and the drain held at or near absolute zero, a problem outside the scope of linear response theory. We obtain local temperatures close to absolute zero when electrons originating from the finite temperature reservoir undergo destructive quantum interference. The local temperature is computed by numerically solving a nonlinear system of equations describing equilibration of a scanning thermoelectric probe with the system, and we obtain excellent agreement with analytic results derived using the Sommerfeld expansion. A local entropy for a nonequilibrium quantum system is introduced, and used as a metric quantifying the departure from local equilibrium. It is shown that the local entropy of the system tends to zero when the probe temperature tends to zero, consistent with the third law of thermodynamics.
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