Relation to a realistic microscopic description

Ignoring quantum effects in a microscopic description we fix the configuration of a. many particle system by prescribing spatial coordinates, momenta, and internal degrees of freedom of all the particles. In statistical mechanics we then define the probability of finding a specific configuration as 

Here Ti is the Hamiltonian of the system, which gives the energy of the configuration considered, and the normalization factor Z is the (canonical) partition function. By construction,. F is a probability density, normahzed to 1 with respect to integration over all the degrees of freedom. 

In tlni last expression we used the power law 7i. For u 0.59 this 

Keeping s fixed, we obviously can apply the above discussion. 

We now turn to our choice of the chain part which clearly reduces to a sum over all chains in the solution. 

The guiding principle in writing down the self-repelling Gaussian chain model is mathematical simplicity, not microscopic faithfulness. Do we have, any idea why such a primitive model properly can explain the experiments To investigate this question we consider how a realistic microscopic description could be reduced to our model. 

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