First part of Homework T08

I am still working on two additional problems for Tarea 08. But meanwhile I want to share with you the first problem:


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  1. Salvador Jiménez27 de abril de 2020 a las 12:59 p.m.

    Excuse me professor, I have two questions.

    1. Why is it written that instead of considering N=N(μ) we consider μ= μ(N) but then for the partial derivative of S with respect to μ there is a chain rule that includes N as a function of μ? Where is the variable substitution reflected? this part is confusing to me.

    2. What is the initial condition that is mentioned in a)? Is it that U and X are constant? does it refer to the thermodynamic limit?

    ResponderBorrar
  2. Thomas27 de abril de 2020 a las 8:01 p.m.

    Thanks for the questions.
    1. I wrote "That is, instead of considering N = N(mu) we consider mu = mu(N)". This is indead misleading. It should rather say the opposite: "We then consider N = N(mu)". The idea is solving the differential equation for that function and then isolate mu as a function of N and the other variables, U and X which are kept fixed.

    2. A general solution of the differential equation will be of the form

    N(mu,U,X ) = N(mu0,U,X) + some function of mu,U,X which is zero at mu = mu0

    I don't know yet the form of the solution. So it is hard to tell where to place the initial value. I.e. how to chose mu0.

    ResponderBorrar

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