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Integrating out fast degrees of freedom is known to yield, to a good approximation, memory-less, i.e. Markovian, dynamics. In the presence of such a time-scale separation local detailed balance is believed to emerge and to guarantee thermodynamic consistency arbitrarily far from equilibrium. Here we present a transparent example of a Markov model of a molecular motor where local detailed balance can be violated despite a clear time-scale separation and hence Markovian dynamics. Driving thearXiv:2111.14734v2 fatcat:iylot7kq6zhgdi3qhwvq72deqy