Universal relations and bounds for fluctuations in quasistatic small heat engines
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arXiv
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| Format: | Preprint |
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2019
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| author | Ito, Kosuke Xu, Guo-Hua Jiang, Chao Roldán, Édgar Rica-Alarcón, Raúl A. Martínez, Ignacio A. Watanabe, Gentaro |
| author_facet | Ito, Kosuke Xu, Guo-Hua Jiang, Chao Roldán, Édgar Rica-Alarcón, Raúl A. Martínez, Ignacio A. Watanabe, Gentaro |
| contents | The efficiency of any heat engine, defined as the ratio of average work output to heat input, is bounded by Carnot's celebrated result. However, this measure is insufficient to characterize the properties of miniaturized heat engines carrying non-negligible fluctuations, and a study of higher-order statistics of their energy exchanges is required. Here, we generalize Carnot's result for reversible cycles to arbitrary order moment of the work and heat fluctuations. Our results show that, in the quasistatic limit, higher-order statistics of a small engine's energetics depend solely on the ratio between the temperatures of the thermal baths. We further prove that our result for the second moment gives universal bounds for the ratio between the variances of work and heat for quasistatic cycles. We test this theory with our previous experimental results of a Brownian Carnot engine and observe the consistency between them, even beyond the quasistatic regime. Our results can be exploited in the design of thermal nanomachines to reduce their fluctuations of work output without marginalizing its average value and efficiency. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_1910_08096 |
| institution | arXiv |
| publishDate | 2019 |
| record_format | arxiv |
| spellingShingle | Universal relations and bounds for fluctuations in quasistatic small heat engines Ito, Kosuke Xu, Guo-Hua Jiang, Chao Roldán, Édgar Rica-Alarcón, Raúl A. Martínez, Ignacio A. Watanabe, Gentaro Statistical Mechanics Classical Physics The efficiency of any heat engine, defined as the ratio of average work output to heat input, is bounded by Carnot's celebrated result. However, this measure is insufficient to characterize the properties of miniaturized heat engines carrying non-negligible fluctuations, and a study of higher-order statistics of their energy exchanges is required. Here, we generalize Carnot's result for reversible cycles to arbitrary order moment of the work and heat fluctuations. Our results show that, in the quasistatic limit, higher-order statistics of a small engine's energetics depend solely on the ratio between the temperatures of the thermal baths. We further prove that our result for the second moment gives universal bounds for the ratio between the variances of work and heat for quasistatic cycles. We test this theory with our previous experimental results of a Brownian Carnot engine and observe the consistency between them, even beyond the quasistatic regime. Our results can be exploited in the design of thermal nanomachines to reduce their fluctuations of work output without marginalizing its average value and efficiency. |
| title | Universal relations and bounds for fluctuations in quasistatic small heat engines |
| topic | Statistical Mechanics Classical Physics |
| url | https://arxiv.org/abs/1910.08096 |