Extrapolating the thermodynamic length with finite-time measurements

• URL: http://arxiv.org/abs/2101.02948v1
• Date: Fri, 8 Jan 2021 10:41:29 GMT
• Title: Extrapolating the thermodynamic length with finite-time measurements
• Authors: Jin-Fu Chen and C. P. Sun and Hui Dong
• Abstract summary: The excess work performed in a heat-engine process with given finite operation time tau is bounded by the thermodynamic length. We propose to measure the thermodynamic length mathcalL through the extrapolation of finite-time measurements mathcalL(tau)=int_0tau[P_mathrmex(t)]1/2dt via the excess power P_mathrmex(t).
• Score: 3.163257448717563
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: The excess work performed in a heat-engine process with given finite operation time \tau is 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}(\tau)=\int_{0}^{\tau}[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.

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