Journal article
Theorems pertaining to Fokker–Planck statistical equilibrium for multidimensional stochastic systems
Journal of mathematical physics, v 27(5), pp 1387-1390
May 1986
Abstract
It is shown that a Fokker–Planck equation ∂P/∂t=−∑
n
i=1∂[Q
i
(q)P]/ ∂q
i
+ 1/2 ∑
n
i, j=1σ
i
j
∂2
P/ ∂q
i
∂q
j
with n≥3 may admit an asymptotic steady‐state solution P → P
eq(q) that is independent of t only if the necessary condition min{2(1−2/n)[∫(Q ⋅ σ−
1 ⋅ Q)
n/2 d
n
q]2/n
, [∫Ω‖S‖
n/2 d
n
q]2/n
} >2−1+2/n
π1+1/n
[Γ((n+1)/2)]−2/n
n
2 [det(σ
i
j
)]1/n
is satisfied, where S=S(q) ≡∑
n
i=1∂Q
i
(q)/ ∂q
i
and the second integral is over the q‐space region Ω≡{q ∈ R
n
such that S(q)<0}. In addition, it is demonstrated that the probability distribution P=P(q,t) is localized in q‐space as t→∞ if S is bounded from above by a negative constant.
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Details
- Title
- Theorems pertaining to Fokker–Planck statistical equilibrium for multidimensional stochastic systems
- Creators
- Gerald Rosen - Drexel University
- Publication Details
- Journal of mathematical physics, v 27(5), pp 1387-1390
- Publisher
- American Institute of Physics (AIP)
- Number of pages
- 4
- Resource Type
- Journal article
- Language
- English
- Academic Unit
- Physics
- Web of Science ID
- WOS:A1986C025100028
- Scopus ID
- 2-s2.0-36549092336
- Other Identifier
- 991019173901304721
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Data related to this publication, from InCites Benchmarking & Analytics tool:
- Web of Science research areas
- Physics, Mathematical