dorsal/arxiv
View SchemaQuasiclassical Coarse Graining and Thermodynamic Entropy
| Authors | Murray Gell-Mann, James Hartle |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0609190 |
| URL | https://arxiv.org/abs/quant-ph/0609190 |
| DOI | 10.1103/PhysRevA.76.022104 |
| Journal | Phys.Rev.A76:022104,2007 |
Abstract
Our everyday descriptions of the universe are highly coarse-grained, following only a tiny fraction of the variables necessary for a perfectly fine-grained description. Coarse graining in classical physics is made natural by our limited powers of observation and computation. But in the modern quantum mechanics of closed systems, some measure of coarse graining is inescapable because there are no non-trivial, probabilistic, fine-grained descriptions. This essay explores the consequences of that fact. Quantum theory allows for various coarse-grained descriptions some of which are mutually incompatible. For most purposes, however, we are interested in the small subset of ``quasiclassical descriptions'' defined by ranges of values of averages over small volumes of densities of conserved quantities such as energy and momentum and approximately conserved quantities such as baryon number. The near-conservation of these quasiclassical quantities results in approximate decoherence, predictability, and local equilibrium, leading to closed sets of equations of motion. In any description, information is sacrificed through the coarse graining that yields decoherence and gives rise to probabilities for histories. In quasiclassical descriptions, further information is sacrificed in exhibiting the emergent regularities summarized by classical equations of motion. An appropriate entropy measures the loss of information. For a ``quasiclassical realm'' this is connected with the usual thermodynamic entropy as obtained from statistical mechanics. It was low for the initial state of our universe and has been increasing since.
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"abstract": "Our everyday descriptions of the universe are highly coarse-grained,\nfollowing only a tiny fraction of the variables necessary for a perfectly\nfine-grained description. Coarse graining in classical physics is made natural\nby our limited powers of observation and computation. But in the modern quantum\nmechanics of closed systems, some measure of coarse graining is inescapable\nbecause there are no non-trivial, probabilistic, fine-grained descriptions.\nThis essay explores the consequences of that fact. Quantum theory allows for\nvarious coarse-grained descriptions some of which are mutually incompatible.\nFor most purposes, however, we are interested in the small subset of\n``quasiclassical descriptions\u0027\u0027 defined by ranges of values of averages over\nsmall volumes of densities of conserved quantities such as energy and momentum\nand approximately conserved quantities such as baryon number. The\nnear-conservation of these quasiclassical quantities results in approximate\ndecoherence, predictability, and local equilibrium, leading to closed sets of\nequations of motion. In any description, information is sacrificed through the\ncoarse graining that yields decoherence and gives rise to probabilities for\nhistories. In quasiclassical descriptions, further information is sacrificed in\nexhibiting the emergent regularities summarized by classical equations of\nmotion. An appropriate entropy measures the loss of information. For a\n``quasiclassical realm\u0027\u0027 this is connected with the usual thermodynamic entropy\nas obtained from statistical mechanics. It was low for the initial state of our\nuniverse and has been increasing since.",
"arxiv_id": "quant-ph/0609190",
"authors": [
"Murray Gell-Mann",
"James Hartle"
],
"categories": [
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"hep-th"
],
"doi": "10.1103/PhysRevA.76.022104",
"journal_ref": "Phys.Rev.A76:022104,2007",
"title": "Quasiclassical Coarse Graining and Thermodynamic Entropy",
"url": "https://arxiv.org/abs/quant-ph/0609190"
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