dorsal/arxiv
View SchemaMaximal-entropy-production-rate nonlinear quantum dynamics compatible with second law, reciprocity, fluctuation-dissipation, and time-energy uncertainty relations
| Authors | Gian-Paolo Beretta |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0112046 |
| URL | https://arxiv.org/abs/quant-ph/0112046 |
| Journal | G.P. Beretta, "Maximum entropy production rate in quantum thermodynamics", Journal of Physics: Conference Series, Vol. 237, 012004, 1-32 (2010) |
Abstract
In view of the recent quest for well-behaved nonlinear extensions of the traditional Schroedinger-von Neumann unitary dynamics that could provide fundamental explanations of recent experimental evidence of loss of quantum coherence at the microscopic level, in this paper, together with a review of the general features of the nonlinear quantum (thermo)dynamics I proposed in a series of papers [see references in G.P. Beretta, Found.Phys. 17, 365 (1987)], I show its exact equivalence with the maximal-entropy-production variational-principle formulation recently derived in S. Gheorghiu-Svirschevski, Phys.Rev. A 63, 022105 (2001). In addition, based on the formalism of general interest I developed for the analysis of composite systems, I show how the variational derivation can be extended to the case of a composite system to obtain the general form of my equation of motion, that turns out to be consistent with the demanding requirements of strong separability. Moreover, I propose a new intriguing fundamental ansatz: that the time evolution along the direction of steepest entropy ascent unfolds at the fastest rate compatible with the time-energy Heisenberg uncertainty relation. This ansatz provides a possible well-behaved general closure of the nonlinear dynamics, compatible with the nontrivial requirements of strong separability, and with no need of new physical constants. In any case, the time-energy uncertainty relation provides lower bounds to the internal-relaxation-time functionals and, therefore, upper bounds to the rate of entropy production.
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"abstract": "In view of the recent quest for well-behaved nonlinear extensions of the\ntraditional Schroedinger-von Neumann unitary dynamics that could provide\nfundamental explanations of recent experimental evidence of loss of quantum\ncoherence at the microscopic level, in this paper, together with a review of\nthe general features of the nonlinear quantum (thermo)dynamics I proposed in a\nseries of papers [see references in G.P. Beretta, Found.Phys. 17, 365 (1987)],\nI show its exact equivalence with the maximal-entropy-production\nvariational-principle formulation recently derived in S.\nGheorghiu-Svirschevski, Phys.Rev. A 63, 022105 (2001). In addition, based on\nthe formalism of general interest I developed for the analysis of composite\nsystems, I show how the variational derivation can be extended to the case of a\ncomposite system to obtain the general form of my equation of motion, that\nturns out to be consistent with the demanding requirements of strong\nseparability. Moreover, I propose a new intriguing fundamental ansatz: that the\ntime evolution along the direction of steepest entropy ascent unfolds at the\nfastest rate compatible with the time-energy Heisenberg uncertainty relation.\nThis ansatz provides a possible well-behaved general closure of the nonlinear\ndynamics, compatible with the nontrivial requirements of strong separability,\nand with no need of new physical constants. In any case, the time-energy\nuncertainty relation provides lower bounds to the internal-relaxation-time\nfunctionals and, therefore, upper bounds to the rate of entropy production.",
"arxiv_id": "quant-ph/0112046",
"authors": [
"Gian-Paolo Beretta"
],
"categories": [
"quant-ph"
],
"journal_ref": "G.P. Beretta, \"Maximum entropy production rate in quantum\n thermodynamics\", Journal of Physics: Conference Series, Vol. 237, 012004,\n 1-32 (2010)",
"title": "Maximal-entropy-production-rate nonlinear quantum dynamics compatible with second law, reciprocity, fluctuation-dissipation, and time-energy uncertainty relations",
"url": "https://arxiv.org/abs/quant-ph/0112046"
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