Dwell-Time Renormalization of Propulsion, Kinetic Current Reversal, and Dissipation at Mechanical Stall in a Run–Pause–Reverse Active Brownian Ratchet

We study a minimal active Brownian ratchet in which the internal motility state is resolved as a three–state Markov chain—forward run, non–propelled pause, and reverse run—with every reversal passing through the pause. Coupled to a three–-site, two–temperature ratchet potential, this construction yields an exactly solvable nine—state network in which the trichotomous drive is an internal degree of freedom carrying its own entropy production, rather than a prescribed external fluctuating force. Pause kinetics renormalize the bare propulsion \( v_{0} \) to the dwell–weighted drift \( v_{\mathrm{eff}}=v_{0}(\Pi_{+}-\Pi_{-}) \), which shifts the stall force and can reverse the current at fixed potential and fixed temperatures through residence times alone. At the exact stall force the dissipation remains positive and grows as \( c\,v_{0}^{2} \); we derive this scaling, decompose it into spatial and internal switching channels, and trace it to a general projected–current mechanism valid for any finite Markov network with a projected observable. In the fast–pause limit the model reduces to the two–orientation direct–flip theory with explicit swap rates, and the passive limit recovers the Carnot bounds for heat–engine and refrigerator operation.