Quantum thermodynamics studies quantum effects in thermal machines. Both quantum coherence and quantum correlations have been theoretically shown to be a physical resource able to boost their performance. But when is a heat engine, which cyclically interacts with external reservoirs that unavoidably destroy its phase coherence, really quantum? We here use the Leggett-Garg inequality to assess the nonclassical properties of a paradigmatic two-level Otto engine with quantum friction. We provide the complete phase diagram characterizing the quantumness of the engine as a function of its parameters and distinguish three different phases: a quantum phase separated from a classical phase by a transition regime. We further derive an analytical expression for the quantum-to-classical transition temperature.
Quantum thermodynamics studies quantum effects in thermal machines. Both quantum coherence and quantum correlations have been theoretically shown to be a physical resource able to boost their performance. But when is a heat engine, which cyclically interacts with external reservoirs that unavoidably destroy its phase coherence, really quantum? We here use the Leggett-Garg inequality to assess the nonclassical properties of a paradigmatic two-level Otto engine with quantum friction. We provide the complete phase diagram characterizing the quantumness of the engine as a function of its parameters and distinguish three different phases: a quantum phase separated from a classical phase by a transition regime. We further derive an analytical expression for the quantum-to-classical transition temperature.
We evaluate the role of quantum coherence as a thermodynamic resource in a noisy, Markovian, one-qubit heat engine. By consuming the coherence of noisy quantum states, we demonstrate that the engine can surpass the classical efficiency limit when operating according to a quantum Otto cycle. The engine's non-classical nature is demonstrated by its violation of the Leggett-Garg's temporal correlations inequality. Amplitude damping increases the extractable work under partial thermalization, thereby increasing the efficiency. In contrast, phase damping increases the extractable work under partial thermalization but reduces the efficiency. We implement the entire Otto cycle in a quantum circuit, simulating realistic amplitude and phase damping channels, as well as gate-level noise. We introduce an operational measure of the circuit's thermodynamic cost to establish a direct link between energy consumption and information processing in quantum heat engines.
Quantum heat engines are devices comprised of one or more quantum systems operating cyclically between two heat reservoirs to produce work.Although the laws of quantum mechanics rule these engines, this does not imply that these machines function in a quantum fashion, or exhibit a quantum advantage.Indeed, quantum heat engines have shown a remarkable similarity with classical models, thus raising the question of what is "quantum" in quantum thermodynamics.With the help of the P-representability concept, an expression called classicality function is introduced -allowing us to quantify the degree of non-classicality of a bosonic system.As an illustration, we consider a quantum heat engine consisting of a single bosonic mode as a working substance coupled to a cold thermal and hot squeezed thermal bath.For two specific protocols, i.e., a quantum Otto and a generalized cycle, we show that the non-classicality is a resource that can be used to perform thermodynamical tasks more efficiently.Furthermore, we present a theoretical framework to study how quantum features, such as entanglement or coherence, affect the classical formulations of thermodynamic axioms.
The working substance fueling a quantum heat engine may contain prominent quantum properties such as coherence and nonclassical correlations. In particular, coherence has been somewhat related to quantum friction, whose origin has been mostly associated with the noncommutativity of a driven Hamiltonian at different times. Here, we consider a quantum Otto heat engine operated at finite time and undergoing incomplete thermalization with a heat source. We introduce analytical expressions relating the engine efficiency and extractable power to the coherence measured in the energy basis of the working substance during the engine cycle. We show that coherence, which has been related to an increase in entropy production and irreversibility, can in also be employed to improve the quantum engine performance, mitigating quantum friction. Such an improvement may be achieved by carefully tuning cycle parameters. To illustrate this coherent improvement we performed a numerical analysis in an experimentally feasible example.
The working substance fueling a quantum heat engine may contain coherence in its energy basis, depending on the dynamics of the engine cycle. In some models of quantum Otto heat engines, energy coherence has been associated with entropy production and quantum friction. We considered a quantum Otto heat engine operating at finite time. Coherence is generated and the working substance does not reach thermal equilibrium after interacting with the hot heat reservoir, leaving the working substance in a state with residual energy coherence. We observe an interferencelike effect between the residual coherence (after the incomplete thermalization) and the coherence generated in the subsequent finite-time stroke. We introduce analytical expressions highlighting the role of coherence and examine how this dynamical interference effect influences the engine performance. Additionally, in this scenario in which coherence is present along the cycle, we argue that the careful tuning of the cycle parameters may exploit this interference effect and make coherence acts like a dynamical quantum lubricant. To illustrate this, we numerically consider an experimentally feasible example and compare the engine performance to the performance of a similar engine where the residual coherence is completely erased, ruling out the dynamical interference effect.
We consider a finite-time quantum Otto heat engine that consists of two isochoric (thermal-contact) process, where the system is alternatively coupled to a hot squeezed and a cold thermal reservoir, and two unitary driven strokes, where the system is isolated from these two baths and its von Neumann entropy keeps constant. Both quantum inner friction and coherence are generated along the driven stroke and coherence cannot be fully erased after the finite-time hot isochore. Using full counting statistics, we present the probability distribution functions of heat injection and total work per cycle, which are dependent on the time duration along each process. With these, we derive the analytical expressions for the thermodynamic quantities of the two-level heat engine, such as total work, thermodynamic efficiency, entropy production, and work fluctuations, in which effects of coherence, squeezing, inner friction and finite-time heat exchange are included. We then numerically determine the thermodynamic quantities and the fluctuations using the parameters employed in the experimental implementation. Our results clarify the role of coherence and squeezing in the performance and fluctuations in the quantum Otto engines.
In this chapter, we examine how quantum coherence affects the effectiveness and performance of quantum Otto engines running in nonequilibrium conditions. Energy conversion on a quantum scale can be understood through the use of quantum Otto engines, which employ cyclic thermodynamic processes involving isochoric and adiabatic transformations. We examine how the ability to extract work from thermal reservoirs at different temperatures is impacted by preserving quantum coherence among the engine’s operating states. We investigate the dynamics of coherence under various nonequilibrium conditions and configurations, including changing temperatures and coupling strengths, using the Quantum Master Equation framework. According to our research, engines with improved quantum coherence perform noticeably better than their classical counterparts, allowing for higher efficiencies and more work extraction. We also explore optimization techniques and real-world applications for creating quantum heat engines that make use of coherence as a vital resource. The potential of coherent quantum states in powering next-generation energy systems is highlighted in this work, which connects theoretical developments in quantum thermodynamics with real-world applications.