Beyond the thermodynamic limit: finite-size corrections to state interconversion rates
Thermodynamics is traditionally constrained to the study of macroscopic systems whose energy fluctuations are negligible compared to their average energy. Here, we push beyond this thermodynamic limit by developing a mathematical framework to rigorously address the problem of thermodynamic transform...
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| Format: | Article |
| Language: | English |
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Verein zur Förderung des Open Access Publizierens in den Quantenwissenschaften
2018-11-01
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| Series: | Quantum |
| Online Access: | https://quantum-journal.org/papers/q-2018-11-27-108/pdf/ |
| _version_ | 1818016256296484864 |
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| author | Christopher T. Chubb Marco Tomamichel Kamil Korzekwa |
| author_facet | Christopher T. Chubb Marco Tomamichel Kamil Korzekwa |
| author_sort | Christopher T. Chubb |
| collection | DOAJ |
| description | Thermodynamics is traditionally constrained to the study of macroscopic systems whose energy fluctuations are negligible compared to their average energy. Here, we push beyond this thermodynamic limit by developing a mathematical framework to rigorously address the problem of thermodynamic transformations of finite-size systems. More formally, we analyse state interconversion under thermal operations and between arbitrary energy-incoherent states. We find precise relations between the optimal rate at which interconversion can take place and the desired infidelity of the final state when the system size is sufficiently large. These so-called second-order asymptotics provide a bridge between the extreme cases of single-shot thermodynamics and the asymptotic limit of infinitely large systems. We illustrate the utility of our results with several examples. We first show how thermodynamic cycles are affected by irreversibility due to finite-size effects. We then provide a precise expression for the gap between the distillable work and work of formation that opens away from the thermodynamic limit. Finally, we explain how the performance of a heat engine gets affected when one of the heat baths it operates between is finite. We find that while perfect work cannot generally be extracted at Carnot efficiency, there are conditions under which these finite-size effects vanish. In deriving our results we also clarify relations between different notions of approximate majorisation. |
| first_indexed | 2024-04-14T07:09:39Z |
| format | Article |
| id | doaj.art-d650713898074f43b6e5e2dbbb85179f |
| institution | Directory Open Access Journal |
| issn | 2521-327X |
| language | English |
| last_indexed | 2024-04-14T07:09:39Z |
| publishDate | 2018-11-01 |
| publisher | Verein zur Förderung des Open Access Publizierens in den Quantenwissenschaften |
| record_format | Article |
| series | Quantum |
| spelling | doaj.art-d650713898074f43b6e5e2dbbb85179f2022-12-22T02:06:28ZengVerein zur Förderung des Open Access Publizierens in den QuantenwissenschaftenQuantum2521-327X2018-11-01210810.22331/q-2018-11-27-10810.22331/q-2018-11-27-108Beyond the thermodynamic limit: finite-size corrections to state interconversion ratesChristopher T. ChubbMarco TomamichelKamil KorzekwaThermodynamics is traditionally constrained to the study of macroscopic systems whose energy fluctuations are negligible compared to their average energy. Here, we push beyond this thermodynamic limit by developing a mathematical framework to rigorously address the problem of thermodynamic transformations of finite-size systems. More formally, we analyse state interconversion under thermal operations and between arbitrary energy-incoherent states. We find precise relations between the optimal rate at which interconversion can take place and the desired infidelity of the final state when the system size is sufficiently large. These so-called second-order asymptotics provide a bridge between the extreme cases of single-shot thermodynamics and the asymptotic limit of infinitely large systems. We illustrate the utility of our results with several examples. We first show how thermodynamic cycles are affected by irreversibility due to finite-size effects. We then provide a precise expression for the gap between the distillable work and work of formation that opens away from the thermodynamic limit. Finally, we explain how the performance of a heat engine gets affected when one of the heat baths it operates between is finite. We find that while perfect work cannot generally be extracted at Carnot efficiency, there are conditions under which these finite-size effects vanish. In deriving our results we also clarify relations between different notions of approximate majorisation.https://quantum-journal.org/papers/q-2018-11-27-108/pdf/ |
| spellingShingle | Christopher T. Chubb Marco Tomamichel Kamil Korzekwa Beyond the thermodynamic limit: finite-size corrections to state interconversion rates Quantum |
| title | Beyond the thermodynamic limit: finite-size corrections to state interconversion rates |
| title_full | Beyond the thermodynamic limit: finite-size corrections to state interconversion rates |
| title_fullStr | Beyond the thermodynamic limit: finite-size corrections to state interconversion rates |
| title_full_unstemmed | Beyond the thermodynamic limit: finite-size corrections to state interconversion rates |
| title_short | Beyond the thermodynamic limit: finite-size corrections to state interconversion rates |
| title_sort | beyond the thermodynamic limit finite size corrections to state interconversion rates |
| url | https://quantum-journal.org/papers/q-2018-11-27-108/pdf/ |
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