Monitored quantum unital Otto heat engines: Fluctuations of the released heat and entropy production

El Makouri, Abdelkader, Slaoui, Abdallah, Ahl Laamara, Rachid

Published Jan 1, 2025• 0 citations

Abstract

Recently, we have considered a single-qubit quantum Otto cycle based on arbitrary (non-unitary) unital channels as a heat source. We showed similarly to some works in literature that the ratio of the fluctuations of work (W) and heat absorbed (QM) is lower-and-upper bounded. In this paper, we drive this line of research further and consider the fluctuations of the stochastic heat exchanged (denoted by QC′) with the cold bath. In general, there is another stochastic quantity, which we denote by QC, that gives the same average as QC′− but not higher cumulants. While QC′ is defined through the two-point measurement scheme, i.e., by measuring the energy of the working medium in all four strokes, QC follows from imposing the first of thermodynamics at the stochastic level. Our work has two important results: (i) first, we prove that the measurement of the working medium during three strokes is sufficient to construct the distribution of QC′ (ii) and that the cumulants of the stochastic entropy production denoted by Σ can be inferred from the cumulants of QC.

Related papers

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

Abdelkader El Makouri, Abdallah Slaoui, R. Ahl Laamara

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.

arXiv:2305.10285Physical review. EOct 6, 20239 citations

Bounds on nonequilibrium fluctuations for asymmetrically driven quantum Otto engines

Sandipan Mohanta, Madhumita Saha, B. Prasanna Venkatesh +1 more

For a four-stroke asymmetrically driven quantum Otto engine with working medium modeled by a single qubit, we study the bounds on nonequilibrium fluctuations of work and heat. We find strict relations between the fluctuations of work and individual heat for hot and cold reservoirs in arbitrary operational regimes. Focusing on the engine regime, we show that the ratio of nonequilibrium fluctuations of output work to input heat from the hot reservoir is both upper and lower bounded. As a consequence, we establish a hierarchical relation between the relative fluctuations of work and heat for both cold and hot reservoirs and further make a connection with the thermodynamic uncertainty relations. We discuss the fate of these bounds also in the refrigerator regime. The reported bounds, for such asymmetrically driven engines, emerge once both the time-forward and the corresponding reverse cycles of the engine are considered on an equal footing. We also extend our study and report bounds for a parametrically driven harmonic oscillator Otto engine.

arXiv:2208.05887Physical review. EJul 19, 202312 citations

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

Sandipan Mohanta, Bijay Kumar Agarwalla

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.

arXiv:2307.04348Physical review. EDec 18, 20231 citation

Finite-time quantum Otto engine with a squeezed thermal bath: Role of quantum coherence and squeezing in the performance and fluctuations

Xiao Ping Yang, Dehua Liu, Jizhou He +2 more

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.

arXiv:2205.13290May 26, 20222 citations

Bounds on fluctuations for finite-time quantum Otto cycle

Sushant Saryal, Bijay Kumar Agarwalla

For quantum Otto engine driven quasistatically, we provide exact full statistics of heat and work for a class of working fluids that follow a scale-invariant energy eigenspectra under driving. Equipped with the full statistics we go on to derive a universal expression for the ratio of nth cumulant of output work and input heat in terms of the mean Otto efficiency. Furthermore, for nonadiabatic driving of quantum Otto engine with working fluid consisting of either a (i) qubit or (ii) a harmonic oscillator, we show that the relative fluctuation of output work is always greater than the corresponding relative fluctuation of input heat absorbed from the hot bath. As a result, the ratio between the work fluctuation and the input heat fluctuation receives a lower bound in terms of the square value of the average efficiency of the engine. The saturation of the lower bound is received in the quasistatic limit of the engine.

arXiv:2104.12173Physical review. EJun 25, 202132 citations

Work Fluctuations in Ergotropic Heat Engines

Giovanni Chesi, Chiara Macchiavello, Massimiliano Federico Sacchi

We study the work fluctuations in ergotropic heat engines, namely two-stroke quantum Otto engines where the work stroke is designed to extract the ergotropy (the maximum amount of work by a cyclic unitary evolution) from a couple of quantum systems at canonical equilibrium at two different temperatures, whereas the heat stroke thermalizes back the systems to their respective reservoirs. We provide an exhaustive study for the case of two qutrits whose energy levels are equally spaced at two different frequencies by deriving the complete work statistics. By varying the values of temperatures and frequencies, only three kinds of optimal unitary strokes are found: the swap operator U1, an idle swap U2 (where one of the qutrits is regarded as an effective qubit), and a non-trivial permutation of energy eigenstates U3, which indeed corresponds to the composition of the two previous unitaries, namely U3=U2U1. While U1 and U2 are Hermitian (and hence involutions), U3 is not. This point has an impact on the thermodynamic uncertainty relations (TURs), which bound the signal-to-noise ratio of the extracted work in terms of the entropy production. In fact, we show that all TURs derived from a strong detailed fluctuation theorem are violated by the transformation U3.

arXiv:2310.10344EntropyNov 9, 20232 citations