dorsal/arxiv
View SchemaCharacteristics of the Limit Cycle of a Reciprocating Quantum Heat Engine
| Authors | Tova Feldmann, Ronnie Kosloff |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0405171 |
| URL | https://arxiv.org/abs/quant-ph/0405171 |
| DOI | 10.1103/PhysRevE.70.046110 |
Abstract
When a reciprocating heat engine is started it eventually settles to a stable mode of operation. The approach of a first principle quantum heat engine toward this stable limit cycle is studied. The engine is based on a working medium consisting of an ensemble of quantum systems composed of two coupled spins. A four stroke cycle of operation is studied, with two {\em isochore} branches where heat is transferred from the hot/cold baths and two {\em adiabats} where work is exchanged. The dynamics is generated by a completely positive map. It has been shown that the performance of this model resembles an engine with intrinsic friction. The quantum conditional entropy is employed to prove the monotonic approach to a limit cycle. Other convex measures, such as the quantum distance display the same monotonic approach. The equations of motion of the engine are solved for the different branches and are combined to a global propagator that relates the state of the engine in the beginning of the cycle to the state after one period of operation of the cycle. The eigenvalues of the propagator define the rate of relaxation toward the limit cycle. A longitudinal and transverse mode of approach to the limit cycle is identified. The entropy balance is used to explore the necessary conditions which lead to a stable limit cycle. The phenomena of friction can be identified with a zero change in the von Neumann entropy of the working medium.
{
"annotation_id": "01e2c086-2dbc-4ffd-9d3c-28e71c4191ec",
"date_created": "2026-03-02T18:02:06.404000Z",
"date_modified": "2026-03-02T18:02:06.404000Z",
"file_hash": "3342eee340b2cff77f8120ba4dc104e38962e1e90b6eb5aac7f70b62ac8e32a0",
"private": false,
"record": {
"abstract": "When a reciprocating heat engine is started it eventually settles to a stable\nmode of operation. The approach of a first principle quantum heat engine toward\nthis stable limit cycle is studied. The engine is based on a working medium\nconsisting of an ensemble of quantum systems composed of two coupled spins. A\nfour stroke cycle of operation is studied, with two {\\em isochore} branches\nwhere heat is transferred from the hot/cold baths and two {\\em adiabats} where\nwork is exchanged. The dynamics is generated by a completely positive map. It\nhas been shown that the performance of this model resembles an engine with\nintrinsic friction. The quantum conditional entropy is employed to prove the\nmonotonic approach to a limit cycle. Other convex measures, such as the quantum\ndistance display the same monotonic approach. The equations of motion of the\nengine are solved for the different branches and are combined to a global\npropagator that relates the state of the engine in the beginning of the cycle\nto the state after one period of operation of the cycle. The eigenvalues of the\npropagator define the rate of relaxation toward the limit cycle. A longitudinal\nand transverse mode of approach to the limit cycle is identified. The entropy\nbalance is used to explore the necessary conditions which lead to a stable\nlimit cycle. The phenomena of friction can be identified with a zero change in\nthe von Neumann entropy of the working medium.",
"arxiv_id": "quant-ph/0405171",
"authors": [
"Tova Feldmann",
"Ronnie Kosloff"
],
"categories": [
"quant-ph"
],
"doi": "10.1103/PhysRevE.70.046110",
"title": "Characteristics of the Limit Cycle of a Reciprocating Quantum Heat Engine",
"url": "https://arxiv.org/abs/quant-ph/0405171"
},
"schema_id": "dorsal/arxiv",
"source": {
"execution_id": "5a7be26d-ccec-4a92-a5ad-c5ee695e5371",
"id": "arXiv Dataset IDs",
"type": "Model",
"variant": "snapshot-2026-03-01",
"version": "0.1.0"
},
"user_id": 1000002
}