Definitions for ehrenfest model
ehren·fest mod·el

WikipediaRate this definition:0.0 / 0 votes

1. Ehrenfest model

   The Ehrenfest model (or dog-flea model) of diffusion was proposed by Tatiana and Paul Ehrenfest to explain the second law of thermodynamics. The model considers N particles in two containers. Particles independently change container at a rate λ. If X(t) = i is defined to be the number of particles in one container at time t, then it is a birth-death process with transition rates q i , i − 1 = i λ {\displaystyle q_{i,i-1}=i\,\lambda } for i = 1, 2, ..., N q i , i + 1 = ( N − i ) λ {\displaystyle q_{i,i+1}=(N-i\,)\lambda } for i = 0, 1, ..., N – 1and equilibrium distribution π i = 2 − N ( N i ) {\displaystyle \pi _{i}=2^{-N}{\tbinom {N}{i}}} . Mark Kac proved in 1947 that if the initial system state is not equilibrium, then the entropy, given by H ( t ) = − ∑ i P ( X ( t ) = i ) log ⁡ ( P ( X ( t ) = i ) π i ) , {\displaystyle H(t)=-\sum _{i}P(X(t)=i)\log \left({\frac {P(X(t)=i)}{\pi _{i}}}\right),} is monotonically increasing (H-theorem). This is a consequence of the convergence to the equilibrium distribution.

How to pronounce ehrenfest model?

1. Alex

   US English

   David

   US English

   Mark

   US English

   Daniel

   British

   Libby

   British

   Mia

   British

   Karen

   Australian

   Hayley

   Australian

   Natasha

   Australian

   Veena

   Indian

   Priya

   Indian

   Neerja

   Indian

   Zira

   US English

   Oliver

   British

   Wendy

   British

   Fred

   US English

   Tessa

   South African

How to say ehrenfest model in sign language?

Numerology

1. Chaldean Numerology

   The numerical value of ehrenfest model in Chaldean Numerology is: 2

2. Pythagorean Numerology

   The numerical value of ehrenfest model in Pythagorean Numerology is: 5

References

1. ^ Wikipedia
   https://en.wikipedia.org/wiki/Ehrenfest_Model