We investigate the motion of two overlapping polymers confined in a 2D box. A statistical model is constructed using blob-free-energy arguments. We find spontaneous segregation under the condition L > R([parallel]), and mixing under L < R([parallel]), where L is the length of the box and R([parallel]) is the polymer extension in an infinite slit. The segregation time (τ) is determined by solving a mean first-passage time problem and by performing Monte Carlo simulations. Both show a minimum in τ as a function of L. Although our results are restricted to 2D, the basic mechanism of competition between entropy and confinement leading to the minimum is suggestive of an evolutionary driving force for size selection.
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