The lifetimes of configuration states in statistical physics

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.

The lifetimes of configuration states in statistical physics

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.

Some aspects of the Smoluchowski process

This article deals with the generalized Smoluchowski process, {n(t), t ≧ 0}, defined by the temporal fluctuating of the numbers of randomly moving particles contained in m < ∞ disjoint regions of space. The relationship of the Smoluchowski process {n(t), t ≧ 0} to the emigration–immigration process is discussed and conditions for their equivalence are presented.

Some aspects of the Smoluchowski process

This article deals with the generalized Smoluchowski process, { n (t), t ≧ 0}, defined by the temporal fluctuating of the numbers of randomly moving particles contained in m &lt; ∞ disjoint regions of space. The relationship of the Smoluchowski process { n (t), t ≧ 0} to the emigration–immigration process is discussed and conditions for their equivalence are presented.