Intrinsic randomness of unstable dynamics and Sz.-Nagy-Foias dilation theory
| dc.creator | Gomez, F. | |
| dc.date | 2006-07-17 | |
| dc.date | 2007-03-05 | |
| dc.date.accessioned | 2026-07-07T07:49:51Z | |
| dc.date.available | 2026-07-07T07:49:51Z | |
| dc.description | Misra, Prigogine and Courbage (MPC) demonstrated the possibility of obtaining stochastic Markov processes from deterministic dynamics simply through a "change of representation" which involves no loss of information provided the dynamical system under consideration has a suitably high degree of instability of motion. From a mathematical point of view, MPC theory is a theory of positivity preserving quasi-affine transformations that intertwine the unitary groups associated with deterministic dynamics to contraction semigroups associated with stochastic Markov processes. In this work, dropping the positivity condition, a characterization of the contraction semigroups induced by quasi-affine transformations, the structure of the unitary groups admitting such intertwining relations and a prototype for the quasi-affinities are given on the basis of the Sz.-Nagy-Foiaş dilation theory. The results are applied to MPC theory in the context of statistical mechanics. | |
| dc.description | 25 pages | |
| dc.identifier | https://arxiv.org/abs/math-ph/0607031 | |
| dc.identifier | http://arxiv.org/abs/math-ph/0607031 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/124976 | |
| dc.subject | Mathematical Physics | |
| dc.subject | 47A45; 47A20 | |
| dc.title | Intrinsic randomness of unstable dynamics and Sz.-Nagy-Foias dilation theory | |
| dc.type | text |