Related papers: Non-exponential decays and nonextensivity
We discuss decay of unstable particles and pair annihilation of stable heavy particles that occur in the cosmic medium, from the point of the fundamental microscopic theory. A fully quantum mechanical treatment shows that the effect of…
We study the phenomenon of system size stochastic resonance within the nonequilibrium potential's framework. We analyze three different cases of spatially extended systems, exploiting the knowledge of their nonequilibrium potential, showing…
We present a stability analysis of the classical ideal gas in a new theory of nonextensive statistics and use the theory to understand the phenomena of negative specific heat in some self-gravitating systems. The stability analysis is made…
Small thermodynamic systems exhibit peculiar behavior different from that observed in long-scale systems. Non-equilibrium processes taking place in those systems are strongly influenced by the presence of fluctuations which can be large.…
The rate equation for an arbitrary mth order growth or decay reaction can be expressed in terms of the q-exponential function, with q equal to m. The analysis suggests that a wide variety of reaction rate (kinetic) processes and models, in…
We demonstrate that description of fluctuations observed in multiparticle production processes using Tsallis statistics approach (in which fluctuations are described by the nonextensivity parameter q) leads to a specific sum rule for…
Given an energy-dissipating port-Hamiltonian system, we characterise the exponential decay of the energy via the model ingredients under mild conditions on the Hamiltonian density $\mathcal{H}$. In passing, we obtain generalisations for…
We show that the strength of non-commutativity could play a role in determining the boundary condition of a physical problem. As a toy model we consider the inverse square problem in non-commutative space. The scale invariance of the system…
We investigate the stability properties of an abstract class of semi-linear systems. Our main result establishes rational rates of decay for classical solutions assuming a certain non-uniform observability estimate for the linear part and…
We prove decay estimates for solutions to non-isotropic linear systems of wave equations. The defining feature of these estimates is that they depend only on the commutation properties of the system with the scaling vector field. As…
In our derivation of the second law of thermodynamics from the relation of adiabatic accessibility of equilibrium states we stressed the importance of being able to scale a system's size without changing its intrinsic properties. This…
A strained epitaxial film deposited on a deformable substrate undergoes a morphological instability relaxing the elastic energy by surface diffusion. The nonlinear and nonlocal dynamical equations of such films with wetting interactions are…
The propagation and decay of neutral B-mesons can be described in terms of quantum dynamical semigroups; they provide generalized time-evolutions that take into account possible non-standard effects leading to loss of phase coherence and…
In order to apply thermodynamics to systems in which entropy is not extensive, it has become customary to define generalized entropies. While this approach has been effective, it is not the only possible approach. We suggest that some…
The nonexponential relaxation ocurring in complex dynamics manifested in a wide variety of systems is analyzed through a simple model of diffusion in phase space. It is found that the inability of the system to find its equilibrium state in…
A nonlinear inequality is formulated in the paper. An estimate of the rate of growth/decay of solutions to this inequality is obtained. This inequality is of interest in a study of dynamical systems and nonlinear evolution equations. It can…
We discuss the relation between the quantum-mechanical survival probability of an unstable system in motion and that of the system at rest. The usual definition of the survival probability which takes into account only the time evolution of…
The non-extensive statistical mechanics has been used to describe a variety of complex systems. The maximization of entropy, often used to introduce the non-extensive statistical mechanics, is a formal procedure and does not easily leads to…
In many situations, in all branches of physics, one encounters power-like behavior of some variables which are best described by a Tsallis distribution characterized by a nonextensivity parameter $q$ and scale parameter $T$. However, there…
We consider systems of n particles that move with constant velocity between collisions. Their total momentum but not necessarily their kinetic energy is preserved at collisions. As there are no further constraints, these systems are…