The lifetimes of configuration states in statistical physics

1981 ◽  
Vol 13 (4) ◽  
pp. 704-719
Author(s):  
Harold Ruben
Keyword(s):  
Statistical Physics ◽  
First Passage Time ◽  
Passage Time ◽  
Stochastic Motion ◽  
After Effects ◽  
Standard Problem ◽  
First Case ◽  
Mean Lifetime ◽  
Standard Exponential Distribution ◽  
Smoluchowski Process

The moments and probability distribution of the lifetime of a configuration state relative to m disjoint regions in ℝd for particles under stochastic motion are expressed in terms of the derivatives at the origin of the probability after-effects for the m regions and for the union of the regions, together with the single integrated and the m randomized first-passage-time distributions, relative to the union of the m regions and to the separate complements of the m regions, respectively. The lifetime, suitably normed in terms of the mean lifetime, is shown to have a limiting standard exponential distribution. Finally, the distributions of lifetime when the motion of the particles is either Brownian or such as to generate a persistent generalized Smoluchowski process are discussed; in the first case, the distribution of lifetime reduces to a standard problem in heat conduction, and in the second case the distribution is expressed in terms of an exponential function and the m probability after-effects for the m regions.

The lifetimes of configuration states in statistical physics

1981 ◽  
Vol 13 (04) ◽  
pp. 704-719
Author(s):  
Harold Ruben
Keyword(s):  
Statistical Physics ◽  
First Passage Time ◽  
Passage Time ◽  
Stochastic Motion ◽  
After Effects ◽  
Standard Problem ◽  
First Case ◽  
Mean Lifetime ◽  
Standard Exponential Distribution ◽  
Smoluchowski Process

The moments and probability distribution of the lifetime of a configuration state relative to m disjoint regions in ℝ d for particles under stochastic motion are expressed in terms of the derivatives at the origin of the probability after-effects for the m regions and for the union of the regions, together with the single integrated and the m randomized first-passage-time distributions, relative to the union of the m regions and to the separate complements of the m regions, respectively. The lifetime, suitably normed in terms of the mean lifetime, is shown to have a limiting standard exponential distribution. Finally, the distributions of lifetime when the motion of the particles is either Brownian or such as to generate a persistent generalized Smoluchowski process are discussed; in the first case, the distribution of lifetime reduces to a standard problem in heat conduction, and in the second case the distribution is expressed in terms of an exponential function and the m probability after-effects for the m regions.

scholarly journals First passage dynamics of stochastic motion in heterogeneous media driven by correlated white Gaussian and coloured non-Gaussian noises

2021 ◽  
Author(s):  
Nicholas Mwilu Mutothya ◽  
Yong Xu ◽  
Yongge Li ◽  
Ralf Metzler ◽  
Nicholas Muthama Mutua
Keyword(s):  
Diffusion Coefficient ◽  
Gaussian Noise ◽  
First Passage Time ◽  
Passage Time ◽  
Mean First Passage Time ◽  
Stochastic Motion ◽  
First Passage ◽  
The Mean ◽  
Non Gaussian ◽  
Markovian Systems

Abstract We study the first passage dynamics for a diffusing particle experiencing a spatially varying diffusion coefficient while driven by correlated additive Gaussian white noise and multiplicative coloured non-Gaussian noise. We consider three functional forms for position dependence of the diffusion coefficient: power-law, exponential, and logarithmic. The coloured non-Gaussian noise is distributed according to Tsallis' $q$-distribution. Tracks of the non-Markovian systems are numerically simulated by using the fourth-order Runge-Kutta algorithm and the first passage times are recorded. The first passage time density is determined along with the mean first passage time. Effects of the noise intensity and self-correlation of the multiplicative noise, the intensity of the additive noise, the cross-correlation strength, and the non-extensivity parameter on the mean first passage time are discussed.

Mean Lifetime and First-Passage Time of the Enzyme Species Involved in an Enzyme Reaction. Application to Unstable Enzyme Systems

2008 ◽  
Vol 70 (5) ◽  
pp. 1425-1449 ◽  
Author(s):  
E. Arribas ◽  
A. Muñoz-Lopez ◽  
M. J. Garcia-Meseguer ◽  
A. Lopez-Najera ◽  
L. Avalos ◽  
...  
Keyword(s):  
First Passage Time ◽  
Enzyme Reaction ◽  
Passage Time ◽  
First Passage ◽  
Enzyme Systems ◽  
Mean Lifetime ◽  
Enzyme Species

scholarly journals Limits theorem of first passages times to regenerative processes

2020 ◽  
pp. 57-67
Author(s):  
O. K. Zakusylo ◽  
I. K. Matsak
Keyword(s):  
Asymptotic Behavior ◽  
Queuing Theory ◽  
Statistical Physics ◽  
Extreme Values ◽  
First Passage Time ◽  
Passage Time ◽  
Regenerative Process ◽  
Fixed Number ◽  
Regenerative Processes ◽  
First Passage

The current work continues the author’s investigation in the field of extreme values analysis. The investigation is concerned with the first passage time of a level u for a wide class of regenerative random processes. The common statement of the problem in most of works in the field under consideration dealt with cases when time of observation, t, and u tend to infinity. Alternatively, we investigate the case when t tends to infinity, whereas u is a fixed number. We establish a general limit theorem for the first passage time of a level u by a regenerative process. This topic is closely associated with the asymptotic behavior of extreme values of regenerative processes. In proving the main result, we establish an important lemma concerning the asymptotic behavior of probabilities for a class of random sums, which may be of independent interest. Necessity of the study of such sums occurs in many areas: mathematical reliability theory, queuing theory, some statistical physics problems. In addition, the work provides examples of applications of the obtained general results to some problems, which arise in applied areas: model of counters of type Geiger-Muller, estimation of the reliability of a redundant system with recovery, the problem of the first passage time of a level u by queue length in the queuing system M/M/1.

scholarly journals Mean First-Passage Time on Scale-Free Networks Based on Rectangle Operation

2021 ◽  
Vol 9 ◽  
Author(s):  
Xiaomin Wang ◽  
Jing Su ◽  
Fei Ma ◽  
Bing Yao
Keyword(s):  
Statistical Physics ◽  
First Passage Time ◽  
Passage Time ◽  
Theory And Practice ◽  
Clustering Coefficient ◽  
Mean First Passage Time ◽  
First Passage ◽  
Kirchhoff Index ◽  
Scale Free ◽  
Free Network

The mean first-passage time of random walks on a network has been extensively applied in the theory and practice of statistical physics, and its application effects depend on the behavior of first-passage time. Here, we firstly define a graphic operation, namely, rectangle operation, for generating a scale-free network. In this paper, we study the topological structures of our network obtained from the rectangle operation, including degree distribution, clustering coefficient, and diameter. And then, we also consider the characteristic quantities related to the network, including Kirchhoff index and mean first-passage time, where these characteristic quantities can not only be used to evaluate the properties of our network, but also have remarkable applications in science and engineering.

First passage time for the state of exact chemical equilibrium

1980 ◽  
Vol 45 (3) ◽  
pp. 777-782 ◽  
Author(s):  
Milan Šolc
Keyword(s):  
Chemical Equilibrium ◽  
First Passage Time ◽  
Passage Time ◽  
The State ◽  
Recurrence Time ◽  
First Passage ◽  
First Order ◽  
The Mean ◽  
Passage Times ◽  
Number Of Particles

The establishment of chemical equilibrium in a system with a reversible first order reaction is characterized in terms of the distribution of first passage times for the state of exact chemical equilibrium. The mean first passage time of this state is a linear function of the logarithm of the total number of particles in the system. The equilibrium fluctuations of composition in the system are characterized by the distribution of the recurrence times for the state of exact chemical equilibrium. The mean recurrence time is inversely proportional to the square root of the total number of particles in the system.

scholarly journals Credit Gap Risk in a First Passage Time Model with Jumps

2009 ◽  
Author(s):  
Natalie Packham ◽  
Lutz Schloegl ◽  
Wolfgang M. Schmidt
Keyword(s):  
First Passage Time ◽  
Passage Time ◽  
First Passage ◽  
Time Model ◽  
Gap Risk ◽  
Credit Gap
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