Extrapolating the thermodynamic length with finite-time measurements

Abstract

The excess work performed in a heat-engine process with given finite operation time τis bounded by the thermodynamic length, which measures the distance during the relaxation along a path in the space of the thermodynamic state. Unfortunately, the thermodynamic length, as a guidance for the heat engine optimization, is beyond the experimental measurement. We propose to measure the thermodynamic length \mathcal{L} through the extrapolation of finite-time measurements \mathcal{L}(τ)=\int_{0}^τ[P_{\mathrm{ex}}(t)]^{1/2}dt via the excess power P_{\mathrm{ex}}(t). The current proposal allows to measure the thermodynamic length for a single control parameter without requiring extra effort to find the optimal control scheme. We illustrate the measurement strategy via examples of the quantum harmonic oscillator with tuning frequency and the classical ideal gas with changing volume.

arXiv comment6+7 pages, 3+5 figures

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• Simulating finite-time quantum isothermal processes with generic superconducting quantum circuit
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• Ergodicity Breaking and Scaling Relations for Finite-Time First-Order Phase Transition
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• A Shortcut to Finite-time Memory Erasure
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• Unified approach to power-efficiency trade-off relations of generic thermal machines
• Thermodynamic speed limit for non-adiabatic work and its classical-quantum decomposition