Bounds on fluctuations for finite-time quantum Otto cycle

Fluctuation theorem in the quantum Otto engine with long-range interaction

The fluctuation of the quantum Otto engine has recently received a lot of attention, while applying the many body with a long-range interaction to a quantum heat engine may enhance our ability of controlling it. Using the two-point measurement and its generalization, we explore the fluctuation theorem of work and heat in a single stroke as well as in a cycle. We discover that the fluctuations of work in a cycle as well as fluctuations of heat in a single stroke or cycle can be connected to the fluctuation of work in a single stroke. Then we numerically investigate the effect of a long-range interaction on these fluctuation theorems, and our result shows that the fluctuation can be improved by manipulating the long-range interaction.

Thermodynamic Geometry of Nonequilibrium Fluctuations in Cyclically Driven Transport

Nonequilibrium thermal machines under cyclic driving generally outperform steady-state counterparts. However, there is still lack of coherent understanding of versatile transport and fluctuation features under time modulations. Here, we formulate a theoretical framework of thermodynamic geometry in terms of full counting statistics of nonequilibrium driven transports. We find that, besides the conventional dynamic and adiabatic geometric curvature contributions, the generating function is also divided into an additional nonadiabatic contribution, manifested as the metric term of full counting statistics. This nonadiabatic metric generalizes recent results of thermodynamic geometry in near-equilibrium entropy production to far-from-equilibrium fluctuations of general currents. Furthermore, the framework proves geometric thermodynamic uncertainty relations of near-adiabatic thermal devices, constraining fluctuations in terms of statistical metric quantities and thermodynamic length. We exemplify the theory in experimentally accessible driving-induced quantum chiral transport and Brownian heat pump.

Universal quantum Otto heat machine based on the Dicke model

In this paper we study a quantum Otto thermal machine where the working substance is composed of N identical qubits coupled to a single mode of a bosonic field, where the atoms and the field interact with a reservoir, as described by the so-called open Dicke model. By controlling the relevant and experimentally accessible parameters of the model we show that it is possible to build a universal quantum heat machine (UQHM) that can function as an engine, refrigerator, heater, or accelerator. The heat and work exchanges are computed taking into account the growth of the number N of atoms as well as the coupling regimes characteristic of the Dicke model for several ratios of temperatures of the two thermal reservoirs. The analysis of quantum features such as entanglement and second-order correlation shows that these quantum resources do not affect either the efficiency or the performance of the UQHM based on the open Dicke model. In addition, we show that the improvement in both efficiency and coefficient of performance of our UQHM occurs for regions around the critical value of the phase transition parameter of the model.

Controlling work output and coherence in finite-time quantum Otto engines through monitoring

We examine the role of diagnostic quantum measurements on the work statistics of a finite-time quantum Otto heat engine operated in the steady state. We consider three pointer-based measurement schemes that differ in the number of system-pointer interactions and pointer measurements. We show that the coherence of the working substance and the work output of the engine can be controlled by tuning the monitoring measurements. Moreover, for a working substance consisting of a two-level system we show that while all three schemes reproduce the predictions of the cycle without any monitoring for the average work in the limit of infinitely weak measurement, only two of the schemes can reproduce the two-point projective measurement results in the limit of strong measurement.

Full statistics of nonequilibrium heat and work for many-body quantum Otto engines and universal bounds: A nonequilibrium Green's function approach

We consider a generic four-stroke quantum Otto engine consisting of two unitary and two thermalization strokes with an arbitrary many-body working medium. Using the Schwinger-Keldysh nonequilibrium Green's function formalism, we provide an analytical expression for the cumulant generating function corresponding to the joint probability distribution of nonequilibrium work and heat. The obtained result is valid up to the second order of the external driving amplitude. We then focus on the linear response limit and obtained Onsager's transport coefficients for the generic Otto cycle and show that the traditional fluctuation-dissipation relation for the total work is violated in the quantum domain, whereas for heat it is preserved. This leads to remarkable consequences in obtaining universal constraints on heat and work fluctuations for engine and refrigerator regimes of the Otto cycle and further allows us to make connections to the thermodynamic uncertainty relations. These findings are illustrated using a paradigmatic model that can be feasibly implemented in experiments.

Monitored nonadiabatic and coherent-controlled quantum unital Otto heat engines: First four cumulants

Recently, measurement-based quantum thermal machines have drawn more attention in the field of quantum thermodynamics. However, the previous results on quantum Otto heat engines were either limited to special unital and nonunital channels in the bath stages, or a specific driving protocol at the work strokes and assuming the cycle being time-reversal symmetric, i.e., V^{†}=U (or V=U). In this paper, we consider a single spin-1/2 quantum Otto heat engine, by first replacing one of the heat baths by an arbitrary unital channel, and then we give the exact analytical expression of the characteristic function from which all the cumulants of heat and work emerge. We prove that under the effect of monitoring, ν_{2}>ν_{1} is a necessary condition for positive work, either for a symmetric or asymmetric-driven Otto cycle. Furthermore, going beyond the average we show that the ratio of the fluctuations of work and heat is lower and upper-bounded when the system is working as a heat engine. However, differently from the previous results in the literature, we consider the third and fourth cumulants as well. It is shown that the ratio of the third (fourth) cumulants of work and heat is not upper-bounded by unity nor lower-bounded by the third (fourth) power of the efficiency, as is the case for the ratio of fluctuations. Finally, we consider applying a specific unital map that plays the role of a heat bath in a coherently superposed manner, and we show the role of the initial coherence of the control qubit on efficiency, on the average work and its relative fluctuations.

Precision bound and optimal control in periodically modulated continuous quantum thermal machines

We use Floquet formalism to study fluctuations in periodically modulated continuous quantum thermal machines. We present a generic theory for such machines, followed by specific examples of sinusoidal, optimal, and circular modulations, respectively. The thermodynamic uncertainty relations (TUR) hold for all modulations considered. Interestingly, in the case of sinusoidal modulation, the TUR ratio assumes a minimum at the heat engine to refrigerator transition point, while the chopped random basis optimization protocol allows us to keep the ratio small for a wide range of modulation frequencies. Furthermore, our numerical analysis suggests that TUR can show signatures of heat engine to refrigerator transition, for more generic modulation schemes. We also study bounds in fluctuations in the efficiencies of such machines; our results indicate that fluctuations in efficiencies are bounded from above for a refrigerator and from below for an engine. Overall, this study emphasizes the crucial role played by different modulation schemes in designing practical quantum thermal machines.

Quantum Otto cycle under strong coupling

Quantum heat engines are often discussed under the weak-coupling assumption that the interaction between the system and the reservoirs is negligible. Although this setup is easier to analyze, this assumption cannot be justified on the quantum scale. In this study, a quantum Otto cycle model that can be generally applied without the weak-coupling assumption is proposed. We replace the thermalization process in the weak-coupling model with a process comprising thermalization and decoupling. The efficiency of the proposed model is analytically calculated and indicates that, when the contribution of the interaction terms is neglected in the weak-interaction limit, it reduces to that of the earlier model. The sufficient condition for the efficiency of the proposed model not to surpass that of the weak-coupling model is that the decoupling processes of our model have a positive cost. Moreover, the relation between the interaction strength and the efficiency of the proposed model is numerically examined by using a simple two-level system. Furthermore, we show that our model's efficiency can surpass that of the weak-coupling model under particular cases. From analyzing the majorization relation, we also find a design method of the optimal interaction Hamiltonians, which are expected to provide the maximum efficiency of the proposed model. Under these interaction Hamiltonians, the numerical experiment shows that the proposed model achieves higher efficiency than that of its weak-coupling counterpart.

Unified trade-off optimization of quantum harmonic Otto engine and refrigerator

We investigate quantum Otto engine and refrigeration cycles of a time-dependent harmonic oscillator operating under the conditions of maximum Ω function, a trade-off objective function which represents a compromise between energy benefits and losses for a specific job, for both adiabatic and nonadiabatic (sudden) frequency modulations. We derive analytical expressions for the efficiency and coefficient of performance of the Otto cycle. For the case of adiabatic driving, we point out that in the low-temperature regime, the harmonic Otto engine (refrigerator) can be mapped to Feynman's ratchet and pawl model which is a steady-state classical heat engine. For the sudden switch of frequencies, we obtain loop-like behavior of the efficiency-work curve, which is characteristic of irreversible heat engines. Finally, we discuss the behavior of cooling power at maximum Ω function.

Optimization of asymmetric quantum Otto engine cycles

We consider the optimization of the work output and fluctuations of a finite-time quantum Otto heat engine cycle consisting of compression and expansion work strokes of unequal duration. The asymmetry of the cycle is characterized by a parameter r_{u} giving the ratio of the times for the compression and expansion work strokes. For such an asymmetric quantum Otto engine cycle, with working substance chosen as a harmonic oscillator or a two-level system, we find that the optimal values of r_{u} maximizing the work output and the reliability (defined as the ratio of average work output to its standard deviation) shows discontinuities as a function of the total time taken for the cycle. Moreover we identify cycles of some specific duration where both the work output and the reliability take their largest values for the same value of the asymmetry parameter r_{u}.