dorsal/arxiv
View SchemaStochasticity, decoherence and an arrow of time from the discretization of time?
| Authors | M. C. Valsakumar |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0505045 |
| URL | https://arxiv.org/abs/quant-ph/0505045 |
| DOI | 10.1007/BF02706206 |
| Journal | Pramana: Journal of Physics, 64 (2005) 593 |
Abstract
Certain intriguing consequences of the discreteness of time on the time evolution of dynamical systems are discussed. In the discrete-time classical mechanics proposed here, there is an {\it arrow of time} that follows from the fact that the replacement of the time derivative by the backward difference operator alone can preserve the non-negativity of the phase space density. It is seen that, even for free particles, all the degrees of freedom are {\it correlated} in principle. The forward evolution of functions of phase space variables by a finite number of time steps, in this discrete-time mechanics, depends on the entire continuous-time history in the interval $[0, \infty]$. In this sense, discrete time evolution is {\it nonlocal} in time from a continuous-time point of view. A corresponding quantum mechanical treatment is possible {\it via} the density matrix approach. The interference between non-degenerate quantum mechanical states decays exponentially. This {\it decoherence} is present, in principle, for all systems; however, it is of practical importance only in macroscopic systems, or in processes involving large energy changes.
{
"annotation_id": "7b9978bc-a71f-46b2-a44a-b66348f2ec45",
"date_created": "2026-03-02T18:02:16.021000Z",
"date_modified": "2026-03-02T18:02:16.021000Z",
"file_hash": "45df076cb1fff1bb3b346b885fe113bafaffeb36056fdb7b937ab462b65ae222",
"private": false,
"record": {
"abstract": "Certain intriguing consequences of the discreteness of time on the time\nevolution of dynamical systems are discussed. In the discrete-time classical\nmechanics proposed here, there is an {\\it arrow of time} that follows from the\nfact that the replacement of the time derivative by the backward difference\noperator alone can preserve the non-negativity of the phase space density. It\nis seen that, even for free particles, all the degrees of freedom are {\\it\ncorrelated} in principle. The forward evolution of functions of phase space\nvariables by a finite number of time steps, in this discrete-time mechanics,\ndepends on the entire continuous-time history in the interval $[0, \\infty]$. In\nthis sense, discrete time evolution is {\\it nonlocal} in time from a\ncontinuous-time point of view. A corresponding quantum mechanical treatment is\npossible {\\it via} the density matrix approach. The interference between\nnon-degenerate quantum mechanical states decays exponentially. This {\\it\ndecoherence} is present, in principle, for all systems; however, it is of\npractical importance only in macroscopic systems, or in processes involving\nlarge energy changes.",
"arxiv_id": "quant-ph/0505045",
"authors": [
"M. C. Valsakumar"
],
"categories": [
"quant-ph"
],
"doi": "10.1007/BF02706206",
"journal_ref": "Pramana: Journal of Physics, 64 (2005) 593",
"title": "Stochasticity, decoherence and an arrow of time from the discretization of time?",
"url": "https://arxiv.org/abs/quant-ph/0505045"
},
"schema_id": "dorsal/arxiv",
"source": {
"execution_id": "8d068154-bc85-4fe2-a330-63b6e7bd40d1",
"id": "arXiv Dataset IDs",
"type": "Model",
"variant": "snapshot-2026-03-01",
"version": "0.1.0"
},
"user_id": 1000002
}