The above expression gives the absolute (quantum) entropy of the system. A precise determination of \Omega(\vec R) would require a quantum model for the ideal chain, which is beyond the scope of this article. However, we have already calculated the probability density P(\vec R) associated with the end-to-end vector of the unconstrained ideal chain, above. Since all micro-states of the ideal chain are equally likely to occur, P(\vec R) is proportional to \Omega(\vec R). This leads to the following expression for the classical (relative) entropy of the ideal chain:
