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.

6+7 pages, 3+5 figures

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• Finite-time Landauer principle
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• Thermodynamic Geometry of Nonequilibrium Fluctuations in Cyclically Driven Transport
• Simulating finite-time quantum isothermal processes with generic superconducting quantum circuit
• Geodesic bound of the minimum energy expense to achieve membrane separation within finite time
• Ergodicity Breaking and Scaling Relations for Finite-Time First-Order Phase Transition
• Geodesic path for the optimal nonequilibrium transition: Momentum-independent protocol
• A Shortcut to Finite-time Memory Erasure
• Dagger-Drazin Inverses
• Unified approach to power-efficiency trade-off relations of generic thermal machines
• Thermodynamic speed limit for non-adiabatic work and its classical-quantum decomposition