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Fluctuation Dissipation Theorem

  1. Dec 21, 2015 #1
    1. The problem statement, all variables and given/known data
    We have a system of two coupled Langevin equations
    dr/dt=kr-yrr+nr(t)
    dp/dt=kpr-ypp+np(t)
    where the ki,yi are constants and ni(t) are noise terms satisfying <ni(t)>=0 and <ni(t')ni(t'')>=qiδ(t'-t'') (this is zero if the two indices differ).

    The physical background of these is that it is a model of protein synthesis - r represents the concentration of mRNA and p the concentration of a protein.

    2. Relevant equations
    The concentration of mRNA should obey Poisson statistics in the steady state, which means that in the long time limit we have <r>=<r2>-<r>2.

    3. The attempt at a solution
    I can solve the first equation for <r> and <r2> and apply the above condition to obtain qr=2kr. I can also then plug my expression for r(t) into the second to obtain expressions for <p> and <p2>, however p does not obey Poisson statistics at long times My issue is in finding the value of qp - the answer should be qp=2kpkr/yr but I cannot understand how to extract this from the condition that only r obeys Poisson statistics at long times.
     
  2. jcsd
  3. Dec 26, 2015 #2
    Thanks for the post! This is an automated courtesy bump. Sorry you aren't generating responses at the moment. Do you have any further information, come to any new conclusions or is it possible to reword the post?
     
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