اشترك بالحزمة الذهبية واحصل على وصول غير محدود شمرا أكاديميا
تسجيل مستخدم جديدPoincare Recurrence, Zermelos Second Law Paradox, and Probabilistic Origin in Statistical Mechanics
108
0
0.0
(
0
)
تأليف
P. D. Gujrati
اسأل ChatGPT حول البحث
ﻻ يوجد ملخص باللغة العربية
We show that Poincare recurrence does not mean that the entropy will eventually decrease, contrary to the claim of Zermelo, and that the probabilitistic origin in statistical physics must lie in the external noise, and not the preparation of the system.
قيم البحث
اقرأ أيضاً
In the case of fully chaotic systems the distribution of the Poincarerecurrence times is an exponential whose decay rate is the Kolmogorov-Sinai(KS) entropy.We address the discussion of the same problem, the connection between dynamics and thermodyna
mics,in the case of sporadic randomness,using the Manneville map as a prototype of this class of processes. We explore the possibility of relating the distribution of Poincare recurrence times to `thermodynamics,in the sense of the KS entropy,also in the case of an inverse power law. This is the dynamic property that Zaslavsly [Phys.Today(8), 39(1999)] finds to be responsible for a striking deviation from ordinary statistical mechanics under the form of Maxwells Demon effect. We show that this way of estabi- lishing a connection between thermodynamics and dynamics is valid only in the case of strong chaos. In the case of sporadic randomness, resulting at long times in the Levy diffusion processes,the sensitivity to initial conditions is initially an inverse pow erlaw,but it becomes exponential in the long-time scale, whereas the distribution of Poincare times keeps its inverse power law forever. We show that a nonextensive thermodynamics would imply the Maxwells Demon effect to be determined by memory and thus to be temporary,in conflict with the dynamic approach to Levy statistics. The adoption of heuristic arguments indicates that this effect,is possible, as a form of genuine equilibrium,after completion of the process of memory erasure.
Noethers calculus of invariant variations yields exact identities from functional symmetries. The standard application to an action integral allows to identify conservation laws. Here we rather consider generating functionals, such as the free energy
and the power functional, for equilibrium and driven many-body systems. Translational and rotational symmetry operations yield mechanical laws. These global identities express vanishing of total internal and total external forces and torques. We show that functional differentiation then leads to hierarchies of local sum rules that interrelate density correlators as well as static and time direct correlation functions, including memory. For anisotropic particles, orbital and spin motion become systematically coupled. The theory allows us to shed new light on the spatio-temporal coupling of correlations in complex systems. As applications we consider active Brownian particles, where the theory clarifies the role of interfacial forces in motility-induced phase separation. For active sedimentation, the center-of-mass motion is constrained by an internal Noether sum rule.
We review phase space techniques based on the Wigner representation that provide an approximate description of dilute ultra-cold Bose gases. In this approach the quantum field evolution can be represented using equations of motion of a similar form t
o the Gross-Pitaevskii equation but with stochastic modifications that include quantum effects in a controlled degree of approximation. These techniques provide a practical quantitative description of both equilibrium and dynamical properties of Bose gas systems. We develo
An interesting connection between the Regge theory of scattering, the Veneziano amplitude, the Lee-Yang theorems in statistical mechanics and nonextensive Renyi entropy is addressed. In this scheme the standard entropy and the Renyi entropy appear to
be different limits of a unique mathematical object. This framework sheds light on the physical origin of nonextensivity. A non trivial application to spin glass theory is shortly outlined.
We review the field of the glass transition, glassy dynamics and aging from a statistical mechanics perspective. We give a brief introduction to the subject and explain the main phenomenology encountered in glassy systems, with a particular emphasis
on spatially heterogeneous dynamics. We review the main theoretical approaches currently available to account for these glassy phenomena, including recent developments regarding mean-field theory of liquids and glasses, novel computational tools, and connections to the jamming transition. Finally, the physics of aging and off-equilibrium dynamics exhibited by glassy materials is discussed.
سجل دخول لتتمكن من نشر تعليقات
التعليقات
جاري جلب التعليقات
سجل دخول لتتمكن من متابعة معايير البحث التي قمت باختيارها
