Abstract
In Chap. 2 we found that the second law of thermodynamics imposes strong restrictions on what can be considered a meaningful thermodynamic measurement. We ask a question motivated by the third law of thermodynamics: What is the coldest possible temperature one can measure in a nonequilibrium quantum system? We have discussed how to measure temperature and voltage in the previous chapter. Most importantly, we realized that temperature and voltage have to be measured simultaneously to ensure uniqueness of the measurement. Here we show that absolute zero cannot be reached for a nonequilibrium quantum system, but arbitrarily low temperatures are, in principle, possible. In quantum coherent conductors, low temperatures result locally when there is destructive interference of “hot” electrons.
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Notes
- 1.
The exact solution to the Eq. (3.30) with T 1 → 0 is
$$\displaystyle \begin{aligned} T_{p}=T_{2}\left(\frac{\sqrt{1 + 4\lambda_{1}^{2}}-1}{2\lambda_{1}}\right)^{\frac{1}{2}}, \end{aligned}$$where λ 1 is defined in Eq. (3.39) and simplifies to
$$\displaystyle \begin{aligned} \lambda_{1}=\frac{7\pi^{2}}{20}\frac{\mathcal{T}_{p2}^{(2)}(k_{B}T_{2})^{2}}{\mathcal{T}_{p1}}, \end{aligned}$$a factor that appears in Eq. (3.32).
- 2.
It is necessary to minimize the ratio of transmissions to find the temperature minima since it is computationally prohibitive to calculate the temperatures at various points in the search space, within each iteration of the optimization algorithm.
- 3.
I would like to thank Justin Bergfield for modeling the tip-sample coupling.
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Shastry, A. (2019). Coldest Measurable Temperature. In: Theory of Thermodynamic Measurements of Quantum Systems Far from Equilibrium. Springer Theses. Springer, Cham. https://doi.org/10.1007/978-3-030-33574-8_3
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