In this paper, we introduce a new class of game dynamics made of a pay-off replicator-like term modulated by an entropy barrier which keeps players away from the boundary of the strategy space. We show that these {\it entropy-driven} dynamics are equivalent to players computing a score as their on-going exponentially discounted cumulative payoff and then using a quantal choice model on the scores to pick an action. This dual perspective on {\it entropy-driven} dynamics helps us to extend the folk theorem on convergence to quantal response equilibria to this case, for potential games. It also provides the main ingredients to design a discrete time effective learning algorithm that is fully distributed and only requires partial information to converge to QRE. This convergence is resilient to stochastic perturbations and observation errors and does not require any synchronization between the players.