  We calculate the spectral gap of the Markov matrix of the totally asymmetric
simple exclusion process (TASEP) on a ring of L sites with N particles. Our
derivation is simple and self-contained and extends a previous calculation that
was valid only for half-filling. We use a special property of the Bethe
equations for TASEP to reformulate them as a one-body problem. Our method is
closely related to the one used to derive exact large deviation functions of
the TASEP.
