Thermal Machines Research Articles

Noise-driven signal study of power systems based on stochastic partial differential equations

The exploration of stochastic partial differential equations in noisy perturbations of dynamical systems remains a major challenge at this stage. The study analyzes the effective dynamical system combining degenerate additive noise-driven stochastic partial differential equations, firstly in the first class of stochastic partial differential equations, the terms in the non-nuclear space formed by nonlinear interactions are overcome by effectively replacing the elements in the non-nuclear space through the ItÔ formulation, and thus the final effective dynamical system is obtained. The effective dynamical system is then obtained in the second type of stochastic partial differential equation using the O-U process similar to the terms in the non-nuclear space. At noise disturbance amplitudes of 5%, 10%, 15% and 20% AC voltage maxima in that order, the effective dynamical systems for the first type of stochastic partial differential equation and the second type of stochastic partial differential equation are more stable compared to the other types of partial differential equation dynamical systems, with the maximum range of error rate improvement for the sampling points 0–239 voltage rms and voltage initial phase value being 3.62% and 26.85% and 2.13% and 19.86% for sampling points 240–360, respectively. The effective dynamic system and stochastic partial differential equation obtained by the research have very high approximation effect, and can be applied to mechanical devices such as thermal power machines.

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.

Quantum heat valve and entanglement in superconducting LC resonators

Quantum superconducting circuit with flexible coupler has been a powerful platform for designing quantum thermal machines. In this Letter, we employ the tunable coupling of two superconducting resonators to realize a heat valve by modulating magnetic flux using a superconducting quantum interference device. It is shown that a heat valve can be realized in a wide parameter range. We find a consistent relation between the heat current and quantum entanglement, which indicates the dominant role of entanglement on the heat valve. It provides an insightful understanding of quantum features in quantum heat machines.

Numerical investigation of flow characteristics and heat transfer efficiency in sawtooth corrugated pipes with Al2O3-CuO/Water hybrid nanofluid

Improvements in heat transfer technologies are a key factor in making all industries that use condensers, solar collectors, and thermal machines more efficient and use less energy. With the development of corrugated pipes that improve convection in an affordable way, passive techniques to optimise heat conduction have entered the market. The objective of this study was to evaluate the performance of a hybrid nanofluid in improving heat transfer efficiency by using corrugated pipes. In particular, we investigated the behaviour of a hybrid nanofluid with a volume concentration of 0.5% Al2O3-CuO/water (80:20 by volume). To investigate the characteristics of the hybrid nanofluid, we used sawtooth-shaped corrugated pipes with different pitch height and pitch distance. The results show that increasing the Reynolds number improves the heat transfer due to higher flow velocities and disturbances from the corrugated surfaces. In terms of the Nusselt number, which is an indicator of convective heat transfer, corrugated pipes consistently perform better than smooth pipes. The average Nusselt number increases between 8% and 74% for the sawtooth-shape corrugated pipes which depends on the pitch height, pitch distance, and Re. However, the presence of corrugations leads to increased friction factors and pressure drops compared to smooth pipes, with larger corrugation amplitudes exacerbating these effects. Shorter pitch distances result in higher Nusselt numbers due to increased flow turbulence and mixing, while longer pitch distances lead to lower Nusselt numbers. These results contribute to the understanding of the effects of pitch height and pitch spacing on corrugated pipe performance. They also provide insights for the design optimisation of efficient heat transfer systems.

Efficiency and thermodynamic uncertainty relations of a dynamical quantum heat engine

In the quest for high-performance quantum thermal machines, looking for an optimal thermodynamic efficiency is only part of the issue. Indeed, at the level of quantum devices, fluctuations become extremely relevant and need to be taken into account. In this paper we study the thermodynamic uncertainty relations for a quantum thermal machine with a quantum harmonic oscillator as a working medium, connected to two thermal baths, one of which is dynamically coupled. We show that parameters can be found such that the machine operates both as a quantum engine or refrigerator, with both sizeable efficiency and small fluctuations.

Modeling Processes of Emergence and Growth of Fractal Structures and Chamber Defects of Thermal Power Units. Part 2

The paper describes further development of model studies with the purpose to draw analogies of the occurrence of possible inhomogeneities and defects of the fractal type on the surface of various objects under the action of laser radiation for different conditions and schemes of a laser simulation experiment in comparison with real processes in the chambers of thermal machines due to the contacts of the working substances with their surface. The subject of this consideration is related to the fact that in laser schemes one can relatively easily and in a controlled manner to study their topology in various modifications (in the range of 0D–3D structures formed on surfaces of various geometric shapes of the fractal type). This provides great opportunities for studying various frequently occurring undesirable random defects and inhomogeneities of complex configuration with the development of unexpected processes in the dynamic modes of operation of various types of power units in their actual operation. This is determined by geometric analysis within the framework of the correspondding non-linear models with different non-linear fractal images. In this aspect, we have used two models to consider the development of emerging fractal fractured structures: first, diffusion propagation/growth of cracks of different geometry with a set of local segments and fragments in different directions; secondly, with diffusely limited aggregation of their distribution (Diffusion-Limited Aggregation – DLA) using the formalism of cellular automata in percolation approximation for different algorithms for the formation of fractal structures. We present only the final results of calculations without details of their procedure, which is sufficient for a visual and qualitative determination of the process of growth of fracturing and defects. In this case, the final goal of consideration is to study the emergence of possible and controllable local areas / collectors, starting from surface structures, and their association with real objects on the surface of chambers with a working substance in power systems. The possible practical significance of such modeling and analysis is discussed to forecast their working conditions.

Model-free optimization of power/efficiency tradeoffs in quantum thermal machines using reinforcement learning.

A quantum thermal machine is an open quantum system that enables the conversion between heat and work at the micro or nano-scale. Optimally controlling such out-of-equilibrium systems is a crucial yet challenging task with applications to quantum technologies and devices. We introduce a general model-free framework based on reinforcement learning to identify out-of-equilibrium thermodynamic cycles that are Pareto optimal tradeoffs between power and efficiency for quantum heat engines and refrigerators. The method does not require any knowledge of the quantum thermal machine, nor of the system model, nor of the quantum state. Instead, it only observes the heat fluxes, so it is both applicable to simulations and experimental devices. We test our method on a model of an experimentally realistic refrigerator based on a superconducting qubit, and on a heat engine based on a quantum harmonic oscillator. In both cases, we identify the Pareto-front representing optimal power-efficiency tradeoffs, and the corresponding cycles. Such solutions outperform previous proposals made in the literature, such as optimized Otto cycles, reducing quantum friction.

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.

Deriving lower bounds on the efficiency of near-degenerate thermal machines via synchronization

Deriving lower bounds on the efficiency of near-degenerate thermal machines via synchronization

Cooperation and Competition in Synchronous Open Quantum Systems.

Synchronization between limit cycle oscillators can arise through entrainment to an external drive or through mutual coupling. The interplay between the two mechanisms has been studied in classical synchronizing systems, but not in quantum systems. Here, we point out that competition and cooperation between the two mechanisms can occur due to phase pulling and phase repulsion in quantum systems. We study their interplay in collectively driven degenerate quantum thermal machines and show that these mechanisms either cooperate or compete depending on the working mode of the machine (refrigerator or engine). The entrainment-mutual synchronization interplay persists with an increase in the number of degenerate levels, while in the thermodynamic limit of degeneracy, mutual synchronization dominates. Overall, our work investigates the effect of degeneracy and multilevel scaling of quantum synchronization and shows how different synchronizing mechanisms can cooperate and compete in quantum systems.

Efficiency at Maximum Power of a Carnot Quantum Information Engine

Optimizing the performance of thermal machines is an essential task of thermodynamics. We here consider the optimization of information engines that convert information about the state of a system into work. We concretely introduce a generalized finite-time Carnot cycle for a quantum information engine and optimize its power output in the regime of low dissipation. We derive a general formula for its efficiency at maximum power valid for arbitrary working media. We further investigate the optimal performance of a qubit information engine subjected to weak energy measurements.

Sustainability framework of intelligent social houses with a synergy of double-façade architecture and active air conditioning systems

Social houses are built around the world to fulfill the basic needs of the growing population, especially middle-income families. Owing to the low budget available for such houses around the globe, necessary energy codes are often compromised. This research, through a methodological sustainability framework, presents the case study of Mexico with the objective to address this worldwide issue. More than 100,000 social houses were built in Mexico just in the year 2021 without strictly following any definitive building energy codes. Eventually, this is a ticking bomb, if left unaddressed, that can bring serious energy and environmental consequences connected with various social issues. Thus, as a research gap, the conventional 4E (energy, exergy, economic, and environmental) analysis cannot fully address such a complex energy-environmental-economic-social nexus. This work proposes an integrated sustainability framework of the practicability of the bioclimatic architecture of such a social house including energy, economic, environmental, and social assessment (novel addition to the analysis). The novel methodology is implemented on a novel technological advancement where double-façade architecture (i.e., solar chimney) is installed through a synergy and intelligent operation with an active air conditioning system including a desiccant enhanced air cooler and novel dew-point evaporative cooler. The article makes use of conventional physics-based modeling of thermal machines combined with an artificial neural network digital twin-based data-driven non-sorting genetic optimization of solar chimneys for various climatic conditions of Mexico. The optimal points are evaluated using annual climatic data to maintain the thermal comfort conditions and the results have suggested an increase of ∼48% through intelligent integration of double-façade architecture with the Maisotsenko cycle air cooler. Life-cycle economic assessment has suggested the Levelized cost of air conditioning be between 0.0096 and 0.0390 USD/kWh and can save up to ∼273 MXN per month with a real payback period of ∼8 years. Environment assessment has reported mitigation of up to ∼5668.59 kgCO2/year as compared to conventional vapor compression refrigeration systems. The social assessment is conducted on a pilot scale to directly ask the people of Mexico about their perception of the installation of the solar chimney while giving the fact that the initial price of the social houses can increase between 2.5 and 4%. It is reported that ∼62% of the sample is willing to install it even with a high price tag with a motive to initiate the climate change mitigation phenomena. The importance of the work has concluded that the government needs to take drastic and tough decisions to further regulate the energy efficiency in the social houses and limit the constructors to offer sustainable building construction.

Thermoelectric efficiency in multiterminal quantum thermal machines from steady-state density functional theory

The multi-terminal generalization of the steady-state density functional theory for the description of electronic and thermal transport (iq-DFT) is presented. The linear response regime of the framework is developed leading to exact expressions for the many-body transport coefficients and thermoelectric efficiency purely in terms of quantities accessible to the framework. The theory is applied to a multi-terminal interacting quantum dot in the Coulomb blockade regime for which accurate parametrizations of the exchange-correlation kernel matrix are given. The thermoelectric efficiency and output power of the multi-terminal system are studied. Surprisingly, the strong-interaction limit of these quantities can be understood in terms of the non-interacting one.

Quantum thermodynamics with fast driving and strong coupling via the mesoscopic leads approach

Understanding the thermodynamics of driven quantum systems strongly coupled to thermal baths is a central focus of quantum thermodynamics and mesoscopic physics. A variety of different methodological approaches exist in the literature, all with their own advantages and disadvantages. The mesoscopic leads approach was recently generalised to steady state thermal machines and has the ability to replicate Landauer B\"uttiker theory in the non-interacting limit. In this approach a set of discretised lead modes, each locally damped, provide a markovian embedding for the baths. In this work we further generalise this approach to incorporate an arbitrary time dependence in the system Hamiltonian. Following a careful discussion of the calculation of thermodynamic quantities we illustrate the power of our approach by studying several driven mesoscopic examples coupled to finite temperature fermionic baths, replicating known results in various limits. In the case of a driven non interacting quantum dot we show how fast driving can be used to induce heat rectification.

Multilayer Graphene as an Endoreversible Otto Engine.

We examine the performance of a finite-time, endoreversible Otto heat engine with a working medium of monolayer or multilayered graphene subjected to an external magnetic field. As the energy spectrum of multilayer graphene under an external magnetic field depends strongly on the number of layers, so too does its thermodynamic behavior. We show that this leads to a simple relationship between the engine efficiency and the number of layers of graphene in the working medium. Furthermore, we find that the efficiency at maximum power for bilayer and trilayer working mediums can exceed that of a classical endoreversible Otto cycle. Conversely, a working medium of monolayer graphene displays identical efficiency at maximum power to a classical working medium. These results demonstrate that layered graphene can be a useful material for the construction of efficient thermal machines for diverse quantum device applications.

Spectral properties of size-invariant shape transformation.

Size-invariant shape transformation is a technique of changing the shape of a domain while preserving its sizes under the Lebesgue measure. In quantum-confined systems, this transformation leads to so-called quantum shape effects in the physical properties of confined particles associated with the Dirichlet spectrum of the confining medium. Here we show that the geometric couplings between levels generated by the size-invariant shape transformations cause nonuniform scaling in the eigenspectra. In particular, the nonuniform level scaling, in the direction of increasing quantum shape effect, is characterized by two distinct spectral features: lowering of the first eigenvalue (ground-state reduction) and changing of the spectral gaps (energy level splitting or degeneracy formation depending on the symmetries). We explain the ground-state reduction by the increase in local breadth (i.e., parts of the domain becoming less confined) that is associated with the sphericity of these local portions of the domain. We accurately quantify the sphericity using two different measures: the radius of the inscribed n-sphere and the Hausdorff distance. Due to Rayleigh-Faber-Krahn inequality, the greater the sphericity, the lower the first eigenvalue. Then level splitting or degeneracy, depending on the symmetries of the initial configuration, becomes a direct consequence of size invariance dictating the eigenvalues to have the same asymptotic behavior due to Weyl law. Such level splittings may be interpreted as geometric analogs of Stark and Zeeman effects. Furthermore, we find that the ground-state reduction causes a quantum thermal avalanche which is the underlying reason for the peculiar effect of spontaneous transitions to lower entropy states in systems exhibiting the quantum shape effect. Unusual spectral characteristics of size-preserving transformations can assist in designing confinement geometries that could lead to classically inconceivable quantum thermal machines.

Carnot Battery Based on Brayton Supercritical CO2 Thermal Machines Using Concentrated Solar Thermal Energy as a Low-Temperature Source

Carnot batteries store surplus power as heat. They consist of a heat pump, which upgrades a low-temperature thermal energy storage, a high-temperature storage system for the upgraded thermal energy, and a heat engine that converts the stored high-temperature thermal energy into power. A Carnot battery is proposed based on supercritical CO2 Brayton thermodynamic cycles. The low-temperature storage is a two-tank molten salt system at 380 °C/290 °C fed by a field of parabolic trough collectors. The high-temperature storage consists of another two-tank molten salt system at 589 °C/405 °C. Printed circuit heat exchangers would be required to withstand the high pressure of the cycles, but shell and tube heat exchangers are proposed instead to avoid clogging issues with molten salts. The conventional allocation of high-temperature molten salt heat exchangers is then modified. Using solar energy to enhance the low-temperature thermal source allowed a round-trip efficiency of 1.15 (COP of 2.46 and heat engine efficiency of 46.5%), thus increasing the stored power. The basic configuration has a levelised cost of storage of USD 376/MWh while replacing the shell and tube heat exchangers with hybrid printed circuit heat exchangers is expected to lower the cost to USD 188/MWh.

Quantum thermodynamics in nonequilibrium reservoirs: Landauer-like bound and its implications

We study quantum thermodynamics in nonequilibrium reservoirs (NERs) that are prepared from initially thermal ones via unitary driving processes. Based on the formulation of entropy production in NERs, we establish a Landauer-like bound and show that the bound can be violated under a definite condition depending on the states of NERs. It is found that the breakdown of this Landauer-like bound implies occurrences of several anomalous phenomena in NERs, namely, the efficiency enhancement of quantum thermal machines beyond the Carnot limit, the extraction of work from a single reservoir, and the spontaneous heat flow from a cold reservoir to a hot one. The results are illustrated through a physical model taking the preparation processes of NERs into account. Our work sheds light on the reason and condition of some unusual phenomena occurring in NERs and is helpful for one to prepare effective NERs that can be used as quantum resources to realize certain thermodynamic tasks.

Quadratic enhancement in the reliability of collective quantum engines

In this theoretical proposal, the authors show that collective effects can be harnessed to significantly increase the signal-to-noise ratio, defined as the ratio of mean work output to the standard deviation of work output, for realistic many-body quantum thermal machines.

Thermodynamic geometry of ideal quantum gases: a general framework and a geometric picture of BEC-enhanced heat engines

Thermodynamic geometry provides a physically transparent framework to describe thermodynamic processes in meso- and micro-scale systems that are driven by slow variations of external control parameters. Focusing on periodic driving for thermal machines, we extend this framework to ideal quantum gases. To this end, we show that the standard approach of equilibrium physics, where a grand-canonical ensemble is used to model a canonical one by fixing the mean particle number through the chemical potential, can be extended to the slow driving regime in a thermodynamically consistent way. As a key application of our theory, we use a Lindblad-type quantum master equation to work out a dynamical model of a quantum many-body engine using a harmonically trapped Bose-gas. Our results provide a geometric picture of the Bose–Einstein condensate-induced power enhancement that was previously predicted for this type of engine on the basis of an endoreversible model (Myers et al 2022 New J. Phys. 24 025001). Using an earlier derived universal trade-off relation between power and efficiency as a benchmark, we further show that the Bose-gas engine can deliver significantly more power at given efficiency than an equally large collection of single-body engines. Our work paves the way for a more general thermodynamic framework that makes it possible to systematically assess the impact of quantum many-body effects on the performance of thermal machines.