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... doubts from exercise 1 of the task in question a) I do not finish understanding what we have to do, we just have to write the definition of the standard deviation as in equation 78 but making the considerations that are given in equation 100 ?, and for question b) I'm confused, do we have to find the expression for pressure? that is, we only do the integral of equation 110 ?.

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  1. Thomas2 de abril de 2020 a las 3:39 p.m.

    In that exercise 1, we don't know the mean nor the standard deviation of the single-particle property A_1(vec p_1, vec q_1). But we assume that they exist and that they are finite. So the task is simply to express the mean and the standard deviation of the many-particle property, A(\vec p, \vec q) in terms of the mean and the standard deviation of the single-particle property.
    Once you achieve this, you can check how the fluctuations scale in the thermodynamic limit (that is, in the limit N--> infinity)

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    1. Thomas2 de abril de 2020 a las 3:44 p.m.

      May be I may add the following: The part where you really have to do some work is when you calculate the second moment of the many-particle observable, A(\vec p, \vec q)

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  2. Thomas2 de abril de 2020 a las 3:48 p.m.

    Now, to the question b). Please read the question carefully. You should not calculate the pressure again. You should calculate the frequency with which particles are hitting the surface of area A.To start with, this quantity has different units than the pressure.

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