  The lack of a unique user equilibrium (UE) route flow in traffic assignment
has posed a significant challenge to many transportation applications. The
maximum-entropy principle, which advocates for the consistent selection of the
most likely solution as a representative, is often used to address the
challenge. Built on a recently proposed day-to-day (DTD) discrete-time
dynamical model called cumulative logit (CULO), this study provides a new
behavioral underpinning for the maximum-entropy UE (MEUE) route flow. It has
been proven that CULO can reach a UE state without presuming travelers are
perfectly rational. Here, we further establish that CULO always converges to
the MEUE route flow if (i) travelers have zero prior information about routes
and thus are forced to give all routes an equal choice probability, or (ii) all
travelers gather information from the same source such that the so-called
general proportionality condition is satisfied. Thus, CULO may be used as a
practical solution algorithm for the MEUE problem. To put this idea into
practice, we propose to eliminate the route enumeration requirement of the
original CULO model through an iterative route discovery scheme. We also
examine the discrete-time versions of four popular continuous-time dynamical
models and compare them to CULO. The analysis shows that the replicator dynamic
is the only one that has the potential to reach the MEUE solution with some
regularity. The analytical results are confirmed through numerical experiments.
