Non-equilibrium directed diffusion and inherently irreversible heat engines

We consider models which are symmetric under time-reversal and which produce net currents under parametrical, dichotomous, thermal excitation. The simplest is based on a three-level system, which is the basic unit of a `minimal' thermally driven ratchet. We analyse the system's behaviour under periodic, dichotomous temperature changes and calculate the current, work and efficiency of the engine as functions of the upper and lower temperatures and of the modulation period. The system's behaviour differs greatly from a quasistatically working heat engine (such as based on a Carnot cycle). We discuss how this behaviour arises due to the inherently irreversible nature of the underlying process.