Energy Optimization Of Two-Level Quantum Otto Machines

Abstract

We present the quantum Otto machine under different optimization criterion when function either as a heat engine or a refrigerator. We examine the optimal performance of the heat engine and refrigerator depending on their efficiency, output power and maximum entropy production. For heat engine case, we obtain the expression for the upper and lower bounds efficiencies at maximum power and maximum ecological function. The optimal ecological performance is laying between the maximum efficiency and the maximum power output. On the other hand, the quantum Otto refrigerator coefficient of performance is optimized for three different criterion – cooling power, χ criterion(product of performance and power) and ecological function. We further study the dimen-sionless power loss to the cold reservoir when the machine is operating as a heat engine as well as its counterpart for the refrigerator case. We find that the maximum operation of the heat engine (refrigerator) cycle is when optimized with respect to hot (cold) reservoir frequency.

Quantum Otto engines at relativistic energies

“…The algebra can be considerably simplified by first taking the corresponding high or low temperature limit of the internal energy before applying Eq. (31). For the low-temperature, non-relativistic medium, the power output is given by,…”

“…Since then, the study of quantum heat engines has expanded to a massive range of different systems and implementations. Works have examined the role of coherence [9][10][11][12][13][14][15][16], quantum correlations [17], many-body effects [15,[18][19][20][21], quantum uncertainty [22], degeneracy [23,24], endoreversible cycles [25][26][27], finite-time cycles [14,[28][29][30], energy optimization [31], shortcuts to adiabaticity [13,18,19,[32][33][34][35][36][37][38], efficiency and power statistics [39][40][41], and comparisons between classical and quantum machines [25,[42][43][44]. Implementations have been proposed in harmonically confined single ions [45], magnetic systems [46], atomic clouds [47], transmon qubits [48], optomechanical systems…”

Effect of Heat Leakage on Relativistic Quantum Lenoir Engine Performance with a Massless Boson as Working Substance in the Infinite Potential Box

“…Since the quantum heat engine (QHE) was introduced by Scovil and Schultz-Dubois in 1959 [1], many other publications have been published on this topic with different quantum working substances. The working substances that have been studied are two-level systems [2,3], many-level systems [4][5][6][7], harmonic oscillator systems [8][9][10][11], spin systems [3,12], etc. All the working substances used are in the microscopic realm where the principles of Quantum Mechanics strictly apply to QHE.…”