dorsal/arxiv
View SchemaThermodynamics of bipartite systems: Application to light-matter interactions
| Authors | E. Boukobza D. J. Tannor |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0611173 |
| URL | https://arxiv.org/abs/quant-ph/0611173 |
Abstract
Heat and work for quantum systems governed by dissipative master equations with a time-dependent driving field were introduced in the pioneering work of Alicki [J. Phys. A 12, L103 (1979)]. Alicki's work was in the Schroedinger picture; here we extend these definitions to the Heisenberg and interaction pictures. We show that in order to avoid consistency problems, the full time derivatives in the definitions for heat flux and power (work flux) should be replaced by partial time derivatives. We also present an alternative approach to the partitioning of the energy flux which differs from that of Alicki in that the instantaneous interaction energy with the external field is not included directly. We then proceed to generalize Alicki's definition of power by replacing the original system and its external driving field with a larger, bipartite system, governed by a time-independent Hamiltonian. Using the definition of heat flux and the generalized definition of power, we derive the first law of thermodynamics in differential form, both for the full bipartite system and the partially traced subsystems. Although the second law (Clausius formulation) is satisfied for the full bipartite system, we find that in general there is no rigorous formulation of the second law for the partially traced subsystem unless certain additional requirements are met. Once these requirements are satisfied, however, both the Carnot and the Clausius formulations of the second law are satisfied. We illustrate this thermodynamic analysis on both the simple Jaynes-Cummings model (JCM) and an extended dissipative Jaynes-Cummings model (ED-JCM), which is a model for a quantum amplifier.
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"abstract": "Heat and work for quantum systems governed by dissipative master equations\nwith a time-dependent driving field were introduced in the pioneering work of\nAlicki [J. Phys. A 12, L103 (1979)]. Alicki\u0027s work was in the Schroedinger\npicture; here we extend these definitions to the Heisenberg and interaction\npictures. We show that in order to avoid consistency problems, the full time\nderivatives in the definitions for heat flux and power (work flux) should be\nreplaced by partial time derivatives. We also present an alternative approach\nto the partitioning of the energy flux which differs from that of Alicki in\nthat the instantaneous interaction energy with the external field is not\nincluded directly. We then proceed to generalize Alicki\u0027s definition of power\nby replacing the original system and its external driving field with a larger,\nbipartite system, governed by a time-independent Hamiltonian. Using the\ndefinition of heat flux and the generalized definition of power, we derive the\nfirst law of thermodynamics in differential form, both for the full bipartite\nsystem and the partially traced subsystems. Although the second law (Clausius\nformulation) is satisfied for the full bipartite system, we find that in\ngeneral there is no rigorous formulation of the second law for the partially\ntraced subsystem unless certain additional requirements are met. Once these\nrequirements are satisfied, however, both the Carnot and the Clausius\nformulations of the second law are satisfied. We illustrate this thermodynamic\nanalysis on both the simple Jaynes-Cummings model (JCM) and an extended\ndissipative Jaynes-Cummings model (ED-JCM), which is a model for a quantum\namplifier.",
"arxiv_id": "quant-ph/0611173",
"authors": [
"E. Boukobza D. J. Tannor"
],
"categories": [
"quant-ph"
],
"title": "Thermodynamics of bipartite systems: Application to light-matter interactions",
"url": "https://arxiv.org/abs/quant-ph/0611173"
},
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