We study the thermally activated barrier crossing by long chain molecules, initially confined to one side of an entropic trap. The entropic barrier is assumed to be of Kramers type. The barrier width is considered to be larger than the chain. The latter is in turn assumed to be long enough, so that a continuum description of the chain is applicable throughout the space. The barrier crossing rate is calculated using multidimensional Kramers theory and the functional integral method. For chains having the same total number of segments, the activation energy itself remains constant. However, the preexponential factor depends on the structure of the polymer. Polymers with the same molecular weight but having longer arms can effect larger fluctuations, thereby increasing its chance to cross the barrier. This leads to an almost exponential increase of the rate prefactor with the radius of gyration. The difference in the barrier crossing rates could be effectively exploited for the separation of molecules having architectural differences, for example, DNA of same length but different degrees of supercoiling. This is illustrated by considering star polymers. The Rouse-Ham model is used to analyze the mechanism of the barrier crossing. We show how the rate expression of the Arrhenius type is affected by the long arms of the star chain.