Irreversible performance of a quantum harmonic heat engine

Abstract

The unavoidable irreversible losses of power in a heat engine are found to be\nof quantum origin. Following thermodynamic tradition a model quantum heat\nengine operating by the Otto cycle is analyzed. The working medium of the model\nis composed of an ensemble of harmonic oscillators. A link is established\nbetween the quantum observables and thermodynamical variables based on the\nconcept of canonical invariance. These quantum variables are sufficient to\ndetermine the state of the system and with it all thermodynamical variables.\nConditions for optimal work, power and entropy production show that maximum\npower is a compromise between the quasistatic limit of adiabatic following on\nthe compression and expansion branches and a sudden limit of very short time\nallocation to these branches. At high temperatures and quasistatic operating\nconditions the efficiency at maximum power coincides with the endoreversible\nresult. The optimal compression ratio varies from the square root of the\ntemperature ratio in the quasistatic limit where their reversibility is\ndominated by heat conductance to the temperature ratio to the power of 1/4 in\nthe sudden limit when the irreversibility is dominated by friction. When the\nengine deviates from adiabatic conditions the performance is subject to\nfriction. The origin of this friction can be traced to the noncommutability of\nthe kinetic and potential energy of the working medium.\n