We study two-mode bosonic engines undergoing an Otto cycle. The energy exchange between the two bosonic systems is provided by a tunable unitary bilinear interaction in the mode operators modeling frequency conversion, whereas the cyclic operation is guaranteed by relaxation to two baths at different temperatures after each interacting stage. By means of a two-point-measurement approach we provide the joint probability of the stochastic work and heat. We derive exact expressions for work and heat fluctuations, identities showing the interdependence among average extracted work, fluctuations, and efficiency, along with thermodynamic uncertainty relations between the signal-to-noise ratio of observed work and heat and the entropy production. We outline how the presented approach can be suitably applied to derive thermodynamic uncertainty relations for quantum Otto engines with alternative unitary strokes.
We study two-mode bosonic engines undergoing an Otto cycle. The energy exchange between the two bosonic systems is provided by a tunable unitary bilinear interaction in the mode operators modeling frequency conversion, whereas the cyclic operation is guaranteed by relaxation to two baths at different temperatures after each interacting stage. By means of a two-point-measurement approach we provide the joint probability of the stochastic work and heat. We derive exact expressions for work and heat fluctuations, identities showing the interdependence among average extracted work, fluctuations, and efficiency, along with thermodynamic uncertainty relations between the signal-to-noise ratio of observed work and heat and the entropy production. We outline how the presented approach can be suitably applied to derive thermodynamic uncertainty relations for quantum Otto engines with alternative unitary strokes.
We study energetic exchanges and fluctuations in two-stroke quantum thermodynamic engines where the working fluid is represented by two multilevel quantum systems, i.e., qudits, the heat flow is allowed by relaxation with two thermal reservoirs at different temperatures, and the work exchange is operated by a partial-swap unitary interaction. We identify three regimes of operation (heat engine, refrigerator, and thermal accelerator), present the thermodynamic uncertainty relations between the entropy production and the signal-to-noise ratio of work and heat, and derive the full joint probability of the stochastic work and heat. Our results bridge the gap between two-qubit and two-mode bosonic swap engines, and show which properties are maintained (e.g., a nonfluctuating Otto efficiency) and which are lost for increasing dimension (e.g., small violations of the standard thermodynamic uncertainty relations or the possibility of beating the Curzon-Ahlborn efficiency).
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.
Abstract We study the thermodynamics of two-stroke heat engines where two bosonic modes a and b are coupled by the general nonlinear interaction V θ = exp ( θ a † n b m − θ ∗ a n b † m ) . By adopting the two-point measurement scheme we retrieve the distribution of the stochastic work, and hence the relative fluctuations of the extracted work up to the second order in the coupling θ. We identify the optimal interactions providing large average work with small fluctuations in the operational regime of the heat engine. Then, we consider the specific cases n = 2, m = 1 and n = 1, m = 2 up to the fourth order in θ. We optimize the average work and the signal-to-noise ratio over the frequencies of the bosonic modes and the temperatures of the reservoirs. Finally, we determine the thermodynamic uncertainty relations for these processes in relation with the order of the expansion of the unitary interaction V θ .
We investigate a two-qubit SWAP thermal machine -- a streamlined analogue of the four-stroke Otto cycle -- whose working medium comprises inertially moving Unruh-DeWitt qubit detectors, each coupled to a thermal quantum field bath prepared at a different temperature. In the presence of relative motion between the working medium and the thermal baths, we derive thermodynamic uncertainty relations (TURs) that quantify the trade-off between performance, entropy production, and power fluctuations. Our analysis identifies regimes where relativistic motion leads to stronger violation of classical TURs, previously observed in static quantum setups. In addition, we establish generalized performance bounds for the thermal machine operating as either a heat engine or a refrigerator, and discuss how relativistic motion can enhance their performances beyond the standard Carnot limits defined by rest-frame temperatures.
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.
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.