Miniaturized heat engines constitute a fascinating field of current research. Many theoretical as well as experimental studies are being conducted which involve colloidal particles in harmonic traps as well as bacterial baths acting like thermal baths. These systems are micron sized and are subjected to large thermal fluctuations. Hence for these systems average thermodynamic quantities like work done, heat exchanged and efficiency loose meaning unless otherwise supported by their full probability distributions. Earlier studies on micro-engines are concerned with applying Carnot or Stirling engine protocols to miniaturized systems, where system undergoes typical two isothermal and two adiabatic changes. Unlike these models we study a prototype system of two classical Ising spins driven by time dependent, phase different, external magnetic fields. These spins are simultaneously in contact with two heat reservoirs at different temperatures for the full duration of the driving protocol. Performance of the model as an engine or a refrigerator depends only on a single parameter namely the phase between two external drivings. We study this system in terms of fluctuations in efficiency and coefficient of performance (COP). We find full distributions of these quantities numerically and study the tails of these distributions. We also study reliability of the engine. We find the fluctuations dominate mean values of efficiency and COP, and their probability distributions are broad with power law tails.Introduction: After Feynman's theoretical construction of his famous Ratchet and Pawl machine in [1], due to advancement in nano science, it is now possible to realize miniaturized engines experimentally [2][3][4][5]. Many of the experiments are based on theoretical predictions namely the fluctuation theorems which put bounds on thermodynamic quantities of interests like efficiency of the engines [6,7]. For thermodynamic engines like Carnot or Stirling the fluctuations are usually ignored and most of the physics is obtained from average values of work and heat [8]. These notions however fail in case of microscopic engines. Micro-engines behave differently and the main reason behind this odd behavior are the loud thermal fluctuations. These thermal fluctuations cause energy exchanges of the order of k B T , where k B is the Boltzmann constant and T the ambient temperature. For small systems one can thus not just rely on mean values of work and heat or as a matter of fact any thermodynamic quantity, but one has to look at full probability distributions. To deal with such systems one needs to use the framework of stochastic thermodynamics [9][10][11]. Many studies on such small scale engines have shown that fluctuations in thermodynamic quantities dominate over mean values even in the quasistatic limit [12][13][14][15][16][17][18][19]. Many studies have also looked at full distributions of efficiency [13,14] and also the large deviation functions [20]. Models with feedback control both instantaneous and delayed have also been in...

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A helical resonator serves as a key element for the detection of the trapped charged particles in a Penning trap. In order to compare the performance of the helical resonators, the concept of figure of merit (FOM) was introduced by Ulmer et al. [Nucl. Instrum. Methods Phys. Res., Sect. A 705, 55–60 (2013)]. In this work, we optimized the geometrical parameters of a resonator by numerical simulations keeping its outer dimensions and the diameter of the copper wire fixed and obtained the best possible value of FOM under these constraints. The corresponding 95 MHz helical resonator has been designed and fabricated, and its measured value of FOM is in good agreement with the simulated values. An empirical relationship between the total length of the wire to make the helical coil and the resonance frequency has been obtained. The simulations show that the FOM increases considerably with the increase in the conductivity of the building material, and this would be useful in detecting the feeble trap signal in cryogenic environment.