5 research outputs found
Irreversible Performance of a Quantum Harmonic Heat Engine
The unavoidable irreversible losses of power in a heat engine are found to be
of quantum origin. Following thermodynamic tradition a model quantum heat
engine operating by the Otto cycle is analyzed. The working medium of the model
is composed of an ensemble of harmonic oscillators. A link is established
between the quantum observables and thermodynamical variables based on the
concept of canonical invariance. These quantum variables are sufficient to
determine the state of the system and with it all thermodynamical variables.
Conditions for optimal work, power and entropy production show that maximum
power is a compromise between the quasistatic limit of adiabatic following on
the compression and expansion branches and a sudden limit of very short time
allocation to these branches. At high temperatures and quasistatic operating
conditions the efficiency at maximum power coincides with the endoreversible
result. The optimal compression ratio varies from the square root of the
temperature ratio in the quasistatic limit where their reversibility is
dominated by heat conductance to the temperature ratio to the power of 1/4 in
the sudden limit when the irreversibility is dominated by friction. When the
engine deviates from adiabatic conditions the performance is subject to
friction. The origin of this friction can be traced to the noncommutability of
the kinetic and potential energy of the working medium.Comment: 25 pages, 7 figures. Revision added explicit heat-transfer expression
and extended the discussion on the quantum origin of frictio
The Quantum Harmonic Otto Cycle
The quantum Otto cycle serves as a bridge between the macroscopic world of heat engines and the quantum regime of thermal devices composed from a single element. We compile recent studies of the quantum Otto cycle with a harmonic oscillator as a working medium. This model has the advantage that it is analytically trackable. In addition, an experimental realization has been achieved, employing a single ion in a harmonic trap. The review is embedded in the field of quantum thermodynamics and quantum open systems. The basic principles of the theory are explained by a specific example illuminating the basic definitions of work and heat. The relation between quantum observables and the state of the system is emphasized. The dynamical description of the cycle is based on a completely positive map formulated as a propagator for each stroke of the engine. Explicit solutions for these propagators are described on a vector space of quantum thermodynamical observables. These solutions which employ different assumptions and techniques are compared. The tradeoff between power and efficiency is the focal point of finite-time-thermodynamics. The dynamical model enables the study of finite time cycles limiting time on the adiabatic and the thermalization times. Explicit finite time solutions are found which are frictionless (meaning that no coherence is generated), and are also known as shortcuts to adiabaticity.The transition from frictionless to sudden adiabats is characterized by a non-hermitian degeneracy in the propagator. In addition, the influence of noise on the control is illustrated. These results are used to close the cycles either as engines or as refrigerators. The properties of the limit cycle are described. Methods to optimize the power by controlling the thermalization time are also introduced. At high temperatures, the Novikov–Curzon–Ahlborn efficiency at maximum power is obtained. The sudden limit of the engine which allows finite power at zero cycle time is shown. The refrigerator cycle is described within the frictionless limit, with emphasis on the cooling rate when the cold bath temperature approaches zero
Reflections on Friction in Quantum Mechanics
Distinctly quantum friction effects of three types are surveyed: internalfriction, measurement-induced friction, and quantum-fluctuation-induced friction. We demonstrate that external driving will lead to quantum internal friction, and critique the measurement-based interpretation of friction. We conclude that in general systems will experience internal and external quantum friction over and beyond the classical frictional contributions