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Miniaturized heat engines constitutes a fascinating field of currentresearch. They are being studied theoretically as well as experimentally, withexperiments involving colloidal particles and harmonic traps and even bacterialbaths acting like thermal baths. They are interesting to study because usualequilibrium thermodynamic notions can not be applied directly to these systems.These systems are micron sized or even smaller and they are subjected to laudthermal fluctuations. Thus one needs to study the behavior of such systems interms of these fluctuations. Average thermodynamic quantities like work done,heat exchanged, efficiency loose meaning unless otherwise supported by theirfull probability distributions. Earlier studies on micro-engines are concernedwith applying Carnot or Stirling engine protocols to miniaturized systems,where system undergoes typical two isothermal and two adiabatic changes. Unlikethese models we for the first time, study a prototype system of two classicalIsing spins driven by time dependent, phase different, external magneticfields. These spins are {\it simultaneously} in contact with two heatreservoirs at different temperatures for the full duration of the drivingprotocol. Performance of the model as an engine or a refrigerator depends onlyon a single parameter namely the phase between two external drivings. We studythis system in terms of fluctuations in efficiency and coefficient ofperformance (COP). We also find full distributions of these quantitiesnumerically and also study the tails of these distributions. We also studyreliability of this engine. We find the fluctuations dominate mean values ofefficiency and COP and their probability distributions are broad with power lawtails.

Two coupled, driven Ising spin systems working as an Engine