dorsal/arxiv
View SchemaQuantum thermodynamic Carnot and Otto-like cycles for a two-level system
| Authors | Gian Paolo Beretta |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0703261 |
| URL | https://arxiv.org/abs/quant-ph/0703261 |
| DOI | 10.1209/0295-5075/99/20005 |
| Journal | EPL, 99, 20005 (2012) |
Abstract
From the thermodynamic equilibrium properties of a two-level system with variable energy-level gap $\Delta$, and a careful distinction between the Gibbs relation $dE = T dS + (E/\Delta) d\Delta$ and the energy balance equation $dE = \delta Q^\leftarrow - \delta W^\to$, we infer some important aspects of the second law of thermodynamics and, contrary to a recent suggestion based on the analysis of an Otto-like thermodynamic cycle between two values of $\Delta$ of a spin-1/2 system, we show that a quantum thermodynamic Carnot cycle, with the celebrated optimal efficiency $1 - (T_{low}/T_{high})$, is possible in principle with no need of an infinite number of infinitesimal processes, provided we cycle smoothly over at least three (in general four) values of $\Delta$, and we change $\Delta$ not only along the isoentropics, but also along the isotherms, e.g., by use of the recently suggested maser-laser tandem technique. We derive general bounds to the net-work to high-temperature-heat ratio for a Carnot cycle and for the 'inscribed' Otto-like cycle, and represent these cycles on useful thermodynamic diagrams.
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"abstract": "From the thermodynamic equilibrium properties of a two-level system with\nvariable energy-level gap $\\Delta$, and a careful distinction between the Gibbs\nrelation $dE = T dS + (E/\\Delta) d\\Delta$ and the energy balance equation $dE =\n\\delta Q^\\leftarrow - \\delta W^\\to$, we infer some important aspects of the\nsecond law of thermodynamics and, contrary to a recent suggestion based on the\nanalysis of an Otto-like thermodynamic cycle between two values of $\\Delta$ of\na spin-1/2 system, we show that a quantum thermodynamic Carnot cycle, with the\ncelebrated optimal efficiency $1 - (T_{low}/T_{high})$, is possible in\nprinciple with no need of an infinite number of infinitesimal processes,\nprovided we cycle smoothly over at least three (in general four) values of\n$\\Delta$, and we change $\\Delta$ not only along the isoentropics, but also\nalong the isotherms, e.g., by use of the recently suggested maser-laser tandem\ntechnique. We derive general bounds to the net-work to high-temperature-heat\nratio for a Carnot cycle and for the \u0027inscribed\u0027 Otto-like cycle, and represent\nthese cycles on useful thermodynamic diagrams.",
"arxiv_id": "quant-ph/0703261",
"authors": [
"Gian Paolo Beretta"
],
"categories": [
"quant-ph"
],
"doi": "10.1209/0295-5075/99/20005",
"journal_ref": "EPL, 99, 20005 (2012)",
"title": "Quantum thermodynamic Carnot and Otto-like cycles for a two-level system",
"url": "https://arxiv.org/abs/quant-ph/0703261"
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