Loss of Temporal Homogeneity and Symmetry in Statistical Systems: Deterministic Versus Stochastic Dynamics

Loss of Temporal Homogeneity and Symmetry in Statistical Systems: Deterministic {protect

A detailed analysis of deterministic (one-to-one) and stochastic (one-to-many) dynamics establishes that dS/dt > 0 is only consistent with the latter, which contains violation of temporal symmetry and homogeneity. We observe that the former only supports dS/dt = 0 and cannot give rise to Boltzmann’s molecular chaos assumption. The ensemble average is more meaningful than the temporal average, e...

Deterministic Versus Stochastic Explanations

Oxygen isotope data for a Pliocene interval from 3.6 to 2.8 million years ago show a mean increase (0.5 per mil) of benthic 6180 at about 3.2 million years ago, whereas planktic 6180 does not increase. This lack of covariance indicates that the event at 3.2 million years did not result in a permanent increase in the ice budget of either the Northern or the Southern Hemisphere. The history of co...

Stochastic versus Deterministic Approaches

Reconstruction of the Deterministic Dynamics of Stochastic Systems

We show that based on the mathematics of Markow processes and in particular based on the definition of Kramers-Moyal coefficients it is possible to estimate the deterministic part of the dynamics for a broad class of nonlinear noisy systems. In particular we show that for different kinds of noise perturbations, including non Langevin force with finite correlation time and independent measuremen...

the study of bright and surface discrete cavity solitons dynamics in saturable nonlinear media

امروزه سالیتون ها بعنوان امواج جایگزیده ای که تحت شرایط خاص بدون تغییر شکل در محیط منتشر می-شوند، زمینه مطالعات گسترده ای در حوزه اپتیک غیرخطی هستند. در این راستا توجه به پدیده پراش گسسته، که بعنوان عامل پهن شدگی باریکه نوری در آرایه ای از موجبرهای جفت شده، ظاهر می گردد، ضروری است، زیرا سالیتون های گسسته از خنثی شدن پراش گسسته در این سیستم ها بوسیله عوامل غیرخطی بوجود می آیند. گسستگی سیستم عامل...