Quantum four-stroke heat engine: Thermodynamic observables in a model with intrinsic friction

Abstract

The fundamentals of a quantum heat engine are derived from first principles. The study is based on the equation of motion of a minimum set of operators which is then used to define the state of the system. The relation between the quantum framework and thermodynamical observables is examined. A four stroke heat engine model with a coupled two-level-system as a working fluid is used to explore the fundamental relations. In the model used, the internal Hamiltonian does not commute with the external control field which defines the two adiabatic branches. Heat is transferred to the working fluid by coupling to hot and cold reservoirs under constant field values.Explicit quantum equation of motion for the relevant observables are derived on all branches. The dynamics on the heat transfer constant field branches is solved in closed form. On the adiabats, a general numerical solution is used and compared with a particular analytic solution. These solutions are combined to construct the cycle of operation. The engine is then analyzed in terms of frequency-entropy and entropy-temperature graphs. The irreversible nature of the engine is the result of finite heat transfer rates and friction-like behavior due to noncommutability of the internal and external Hamiltonian.

Implications of Coupling in Quantum Thermodynamic Machines

“…This model is well studied as quantum Otto cycle [24,25]. In terms of raising and lowering operators, we can write the spin Hamiltonian as…”

“…Because, in this case, the eigenvectors of the Hamiltonian are functions of Ω and λ J . Hence, when the system works as Otto cycle, by changing the magnetic field associated with the system, internal friction appears to be depending upon the rate at which magnetic field is changed [24,25]. This is due to the non-commutativity of the Hamiltonian at different instances during the driving.…”

“…The performance of coupled quantum systems as heat engines have been studied widely in recent past [24][25][26][27][28][29][30]. Work and efficiency are two important quantities to characterize the performance of a heat engine.…”

Quantum lubrication: Suppression of friction in a first-principles four-stroke heat engine

“…Whenever the control Hamiltonian does not commute with the internal Hamiltonian of the working medium, the rapid change in the external field does not allow the state of the working medium to follow adiabatically the instantaneous energy levels [10,11,12]. As a result both coherences and additional energy becomes stored in the working medium.…”

“…whereσ represent the spin Pauli operators and J scales the strength of the inter-particle interaction [10,11]. The external control Hamiltonian is chosen as:…”