We study a refrigerator model which consists of two $n$-level systems interacting via a pulsed external field. Each system couples to its own thermal bath at temperatures $T_h$ and $T_c$, respectively ($θ\equiv T_c/T_h<1$). The refrigerator functions in two steps: thermally isolated interaction between the systems driven by the external field and isothermal relaxation back to equilibrium. There is a complementarity between the power of heat transfer from the cold bath and the efficiency: the latter nullifies when the former is maximized and {\it vice versa}. A reasonable compromise is achieved by optimizing the product of the heat-power and efficiency over the Hamiltonian of the two system. The efficiency is then found to be bounded from below by $ζ_{\rm CA}=\frac{1}{\sqrt{1-θ}}-1$ (an analogue of the Curzon-Ahlborn efficiency), besides being bound from above by the Carnot efficiency $ζ_{\rm C} = \frac{1}{1-θ}-1$. The lower bound is reached in the equilibrium limit $θ\to 1$. The Carnot bound is reached (for a finite power and a finite amount of heat transferred per cycle) for $\ln n\gg 1$. If the above maximization is constrained by assuming homogeneous energy spectra for both systems, the efficiency is bounded from above by $ζ_{\rm CA}$ and converges to it for $n\gg 1$.
Based on a quantum thermodynamic protocol for shortcut to isothermality that smoothly modify the system-reservoir interaction can significantly speed up an isothermal process while keeping the overall dissipation constant [Phys. Rev. X. 10, 031015 (2020)], we extend the study of optimization performance of Carnot-like heat engines and refrigerators in a straightforward and unified way. We derive the universal optimization efficiency of heat engines and the optimization coefficient of performance of refrigerators under two unified optimization criterions, i.e., chi criterion and omega criterion…
The derivation of general performance benchmarks is important in the design of highly optimized heat engines and refrigerators. To obtain them, one may model phenomenologically the leading sources of irreversibility ending up with results which are model-independent, but limited in scope. Alternatively, one can take a simple physical system realizing a thermodynamic cycle and assess its optimal operation from a complete microscopic description. We follow this approach in order to derive the coefficient of performance at maximum cooling rate for \textit{any} endoreversible quantum refrigerator.…
We propose a three-qubit setup for the implementation of a variety of quantum thermal machines where all heat fluxes and work production can be controlled. An important configuration that can be designed is that of an absorption refrigerator, extracting heat from the coldest reservoir without the need of external work supply. Remarkably, we achieve this regime by using only two-body interactions instead of the widely employed three-body interactions. This configuration could be more easily realised in current experimental setups. We model the open-system dynamics with both a global and a local…
We have studied the single particle heat engine and refrigerator driven by time asymmetric protocol of finite duration. Our system consists of a particle in a harmonic trap with time-periodic strength that drives the particle cyclically between two baths. Each cycle consists of two isothermal steps at different temperatures and two adiabatic steps connecting them. The system works in irreversible mode of operation even in the quasistatic regime. This is indicated by finite entropy production even in the large cycle time limit. Consequently, Carnot efficiency for heat engine or Carnot Co-effici…
A unified $χ$-criterion for heat devices (including heat engines and refrigerators) which is defined as the product of the energy conversion efficiency and the heat absorbed per unit time by the working substance [de Tomás \emph{et al} 2012 \textit{Phys. Rev. E} \textbf{85} 010104(R)] is optimized for tight-coupling heat engines and refrigerators operating between two heat baths at temperatures $T_c$ and $T_h(>T_c)$. By taking a new convention on the thermodynamic flux related to the heat transfer between two baths, we find that for a refrigerator tightly and symmetrically coupled with two hea…
The rate of temperature decrease of a cooled quantum bath is studied as its temperature is reduced to the absolute zero. The III-law of thermodynamics is then quantified dynamically by evaluating the characteristic exponent ζ of the cooling process dT(t)/dt \sim -T^ζ when approaching the absolute zero, T \rightarrow 0. A continuous model of a quantum refrigerator is employed consisting of a working medium composed either by two coupled harmonic oscillators or two coupled 2-level systems. The refrigerator is a nonlinear device merging three currents from three heat baths: a cold bath to be cool…
We consider absorption refrigerators consisting of simultaneously operating Carnot-type heat engine and refrigerator. Their maximum efficiency at given power (MEGP) is given by the product of MEGPs for the internal engine and refrigerator. The only subtlety of the derivation lies in the fact that the maximum cooling power of the absorption refrigerator is not limited just by the maximum power of the internal refrigerator but, due to the first law, also by that of the internal engine. As a specific example, we consider the simultaneous absorption refrigerators composed of low-dissipation (LD) h…
We proposed a scheme to implement a self-contained quantum refrigerator system composed of three rf-SQUID qubits, or rather, flux-biased phase qubits. The three qubits play the roles of the target, the refrigerator and the heat engine respectively. We provide different effective temperatures for the three qubits, by imposing external current noises of different strengths. The differences of effective temperatures give rise to the flow of free energy and that drives the refrigerator system to cool down the target. We also show that the efficiency of the system approaches the Carnot efficiency.
The three-terminal heat device consisting of a cavity and coupled to a heat bath is established. By tuning the temperatures of the electrodes and the phonon bath, the device can function as a heat engine or a refrigerator. We study the characteristic performance in the linear and nonlinear regime for both setups. It is our focus here to analyze how the efficiency of the heat engine and coefficient of performance of the refrigerator are affected by the nonlinear transport. With such considerations, the maximum efficiency and power are then optimized for various energy levels, temperatures and o…
At the very foundation of the second law of thermodynamics lies the fact that no heat engine operating between two reservoires of temperatures $T_C\leq T_H$ can overperform the ideal Carnot engine: $\langle W \rangle / \langle Q_H \rangle \leq 1-T_C/T_H$. This inequality follows from an exact fluctuation relation involving the nonequilibrium work $W$ and heat exchanged with the hot bath $Q_H$. In a previous work [Sinitsyn N A, J. Phys. A: Math. Theor. {\bf 44} (2011) 405001] this fluctuation relation was obtained under the assumption that the heat engine undergoes a stochastic jump process. He…
Nonlinear refrigerator with a finite-sized cold heat bath
The Institute of Mathematical Sciences（数学科学研究所）；Homi Bhabha National Institute（霍米·巴巴国立研究所）；Division of Sciences, Krea University（克里亚大学理学院）；Department of Complexity Science and Engineering, Graduate School of Frontier Sciences, The University of Tokyo（东京大学前沿科学研究生院复杂科学与工程系）
We present the spin quantum Otto machine under different optimization criterion when function either as a heat engine or a refrigerator. We examine the optimal performance of the heat engine and refrigerator depending on their efficiency, output power and maximum entropy production. For heat engine case, we obtain the expression for the upper and lower bounds efficiencies at maximum power and maximum ecological function. In addition, the spin quantum Otto refrigerator coefficient of performance is optimized for three different criterion -- cooling power, product of performance and power and ec…
We study the optimization of the performance of arbitrary periodically driven thermal machines. Within the assumption of fast modulation of the driving parameters, we derive the optimal cycle that universally maximizes the extracted power of heat engines, the cooling power of refrigerators, and in general any linear combination of the heat currents. We denote this optimal solution as ``generalized Otto cycle'' since it shares the basic structure with the standard Otto cycle, but it is characterized by a greater number of fast strokes. We bound this number in terms of the dimension of the Hilbe…
Quantum refrigerators pump heat from a cold to a hot reservoir. In the few-particle regime, counter-diabatic (CD) driving of, originally adiabatic, work-exchange strokes is a promising candidate to overcome the bottleneck of vanishing cooling power. Here, we present a finite-time many-body quantum refrigerator that yields finite cooling power at high coefficient of performance, that considerably outperforms its non-adiabatic counterpart. We employ multi-spin CD driving and numerically investigate the scaling behavior of the refrigeration performance with system size. We further prove that opti…
We consider a quantum Otto refrigerator cycle of a time-dependent harmonic oscillator. We investigate the coefficient of performance at maximum figure of merit for adiabatic and nonadiabatic frequency modulations. We obtain analytical expressions for the optimal performance both in the high-temperature (classical) regime and in the low-temperature (quantum) limit. We moreover analyze the breakdown of the cooling cycle for strongly nonadiabatic driving protocols and derive analytical estimates for the minimal driving time allowed for cooling.
The energetics of a Brownian heat engine and heat pump driven by position dependent temperature, known as the Büttiker-Landauer heat engine and heat pump, is investigated by numerical simulations of the inertial Langevin equation. We identify parameter values for optimal performance of the heat engine and heat pump. Our results qualitatively differ from approaches based on the overdamped model. The behavior of the heat engine and heat pump, in the linear response regime is examined under finite time conditions and we find that the efficiency is lower than that of an endoreversible engine worki…
We investigate the energetics of a Brownian motor driven by position dependent temperature, commonly known as the B{ü}ttiker-Landauer motor. Overdamped models (M=0) predict that the motor can attain Carnot efficiency. However, the overdamped limit ($M\to 0$), contradicts the previous prediction due to the kinetic energy contribution to the heat transfer. Using molecular dynamics simulation and numerical solution of the inertial Langevin equation, we confirm that the motor can never achieve Carnot efficiency and verify that the heat flow via kinetic energy diverges as $M^{-1/2}$ in the overdamp…
Theoretical thermoelectric nanophysics models of low-dimensional electronic heat engine and refrigerator devices, comprising two-dimensional hot and cold reservoirs and an interconnecting filtered electron transport mechanism have been established. The models were used to numerically simulate and evaluate the thermoelectric performance and energy conversion efficiencies of these low-dimensional devices, based on three different types of electron transport momentum-dependent filters, referred to herein as: kx, ky and kr filters. Assuming the Fermi-Dirac distribution of electrons, expressions fo…
The χ-criterion is defined as the product of the energy conversion efficiency and the heat absorbed per-unit-time by the working substance [de Tomás et al., Phys. Rev. E, 85 (2012) 010104(R)]. The χ-criterion for Feynman ratchet as a refrigerator operating between two heat baths is optimized. Asymptotic solutions of the coefficient of performance at maximum χ-criterion for Feynman ratchet are investigated at both large and small temperature difference. An interpolation formula, which fits the numerical solution very well, is proposed. Besides, the sufficient condition for the universality of t…
Understanding noisy information engines is a fundamental problem of non-equilibrium physics, particularly in biomolecular systems agitated by thermal and active fluctuations in the cell. By the generalized second law of thermodynamics, the efficiency of these engines is bounded by the mutual information passing through their noisy feedback loop. Yet, direct measurement of the interplay between mutual information and energy has so far been elusive. To allow such examination, we explore here the entire phase-space of a noisy colloidal information engine, and study efficiency fluctuations due to …
We theoretically investigate the coefficient of performance (COP) of a mesoscopic thermoelectric refrigerator realized by using a tunnel junction. We analyze the influence of particle and heat current fluctuations on the COP out of the equilibrium regime. We calculate the average COP by using full counting statistics and find that it depends on the measurement time $τ$. The deviation from the macroscopic COP value can be expressed with the Skellam distribution at all times. This result enables us to improve the Gaussian approximation valid within the linear response regime, which cannot predic…
We study the heat transfer between two nanoparticles held at different temperatures that interact through nonreciprocal forces, by combining molecular dynamics simulations with stochastic thermodynamics. Our simulations reveal that it is possible to construct nano refrigerators that generate a net heat transfer from a cold to a hot reservoir at the expense of power exerted by the nonreciprocal forces. Applying concepts from stochastic thermodynamics to a minimal under-damped Langevin model, we derive exact analytical expressions predictions for the fluctuations of work, heat, and efficiency, w…
We study the optimal performance of a three-level quantum refrigerator using two different objective functions: cooling power and $χ$-function. For both cases, we obtain general expressions for the coefficient of performance (COP) and derive its well-known lower and upper bounds for the limiting cases when the ratio of system-bath coupling constants at the hot and cold contacts approaches infinity and zero, respectively. We also show that the cooling power is optimizable only in the local region with respect to one control frequency, while $χ$-function can be optimized globally with respect to…
We study the application of a counter-diabatic driving (CD) technique to enhance the thermodynamic efficiency and power of a quantum Otto refrigerator based on a superconducting qubit coupled to two resonant circuits. Although the CD technique is originally designed to counteract non-adiabatic coherent excitations in isolated systems, we find that it also works effectively in the open system dynamics, improving the coherence-induced losses of efficiency and power. We compare the CD dynamics with its classical counterpart, and find a deviation that arises because the CD is designed to follow th…
We study two models of quantum absorption refrigerators with the main focus on discerning the role of noise-induced coherence on their thermodynamic performance. Analogously to the previous studies on quantum heat engines, we find the increase in the cooling power due to the mechanism of noise-induced coherence. We formulate conditions imposed on the microscopic parameters of the models under which they can be equivalently described by classical stochastic processes and compare the performance of the two classes of fridges (effectively classical vs. truly quantum). We find that the enhanced pe…
We model a microscopic heat engine as a particle hopping on a one-dimensional lattice in a periodic sawtooth potential, with or without load, assisted by the thermal kicks it gets from alternately placed hot and cold thermal baths. We find analytic expressions for current and rate of heat flow when the engine operates at steady state. Three regions are identified where the model acts either as a heat engine or as a refrigerator or as neither of the two. At quasistatic limit both efficiency of the engine and coefficient of performance of the refrigerator go to that for Carnot engine and Carnot …
We discuss the effect of subdividing the ratchet potential on the performance of a tiny Brownian heat engine that is modeled as a Brownian particle hopping in a viscous medium in a sawtooth potential (with or without load) assisted by alternately placed hot and cold heat baths along its path. We show that the velocity, the efficiency and the coefficient of performance of the refrigerator maximize when the sawtooth potential is subdivided into series of smaller connected barrier series. When the engine operates quasistatically, we analytically show that the efficiency of the engine can not appr…
Absorption refrigerators transfer thermal energy from a cold bath to a hot bath without input power by utilizing heat from an additional "work" reservoir. Particularly interesting is a three-level design for a quantum absorption refrigerator, which can be optimized to reach the maximal (Carnot) cooling efficiency. Previous studies of three-level chillers focused on the behavior of the averaged cooling current. Here, we go beyond that and study the full counting statistics of heat exchange in a three-level chiller model. We explain how to obtain the complete cumulant generating function of the …
Maxwell refrigerator as a device that can transfer heat from a cold to hot temperature reservoir making use of information reservoir was introduced by Mandal et al. \cite{Mandal2013a}. The model has a two state demon and a bit stream interacting with two thermal reservoirs simultaneously. We work out a simpler version of the refrigerator where the demon and bit system interact with the reservoirs separately and for a duration long enough to establish equilibrium. The efficiency, $η$, of the device when working as an engine as well as the coefficient of performance (COP) when working as a refri…
Heat engines provide most of our mechanical power and are essential for transportation on macroscopic scale. However, although significant progress has been made in the miniaturization of electrostatic engines, it has proven difficult to reduce the size of liquid or gas driven heat engines below 10^7 um^3. Here we demonstrate that a crystalline silicon structure operates as a cyclic piezoresistive heat engine when it is driven by a sufficiently high DC current. A 0.34 um^3 engine beam draws heat from the DC current using the piezoresistive effect and converts it into mechanical work by expansi…
We apply the model of minimally nonlinear irreversible heat engines developed by Izumida and Okuda [EPL {\bf 97}, 10004 (2012)] to refrigerators. The model assumes extended Onsager relations including a new nonlinear term accounting for dissipation effects. The bounds for the optimized regime under an appropriate figure of merit and the tight-coupling condition are analyzed and successfully compared with those obtained previously for low-dissipation Carnot refrigerators in the finite-time thermodynamics framework. Besides, we study the bounds for the nontight-coupling case numerically. We also…
We study a refrigerator model which consists of two $n$-level systems interacting via a pulsed external field. Each system couples to its own thermal bath at temperatures $T_h$ and $T_c$, respectively ($θ\equiv T_c/T_h<1$). The refrigerator functions in two steps: thermally isolated interaction between the systems driven by the external field and isothermal relaxation back to equilibrium. There is a complementarity between the power of heat transfer from the cold bath and the efficiency: the latter nullifies when the former is maximized and {\it vice versa}. A reasonable compromise is achieved…
We study the optimal performance of a three-level quantum refrigerator using a trade-off objective function, $Ω$ function, which represents a compromise between the energy benefits and the energy losses of a thermal device. First, we optimize the performance of our refrigerator by employing a two-parameter optimization scheme and show that the first two-terms in the series expansion of the obtained coefficient of performance (COP) match with those of some classical models of refrigerator. Then, in the high-temperature limit, optimizing with respect to one parameter while constraining the other…
Refrigerators use a thermodynamic cycle to move thermal energy from a cold reservoir to a hot one. Implementing this operation principle with mesoscopic components has recently emerged as a promising strategy to control heat currents in micro and nano systems for quantum technological applications. Here, we combine concepts from stochastic and quantum thermodynamics with advanced methods of optimal control theory to develop a universal optimization scheme for such small-scale refrigerators. Covering both the classical and the quantum regime, our theoretical framework provides a rigorous proced…
We present a detailed study of a Brownian particle driven by Carnot-type refrigerating protocol operating between two thermal baths. Both the underdamped as well as the overdamped limits are investigated. The particle is in a harmonic potential with time-periodic strength that drives the particle cyclically between the baths. Each cycle consists of two isothermal steps at different temperatures and two adiabatic steps connecting them. Besides working as a stochastic refrigerator, it is shown analytically that in the quasistatic regime the system can also act as stochastic heater, depending on …
We model a tiny heat engine as a Brownian particle that moves in a viscous medium in a sawtooth potential (with or without load) assisted by $\it {alternately}$ placed hot and cold heat baths along its path. We find closed form expression for the steady state current as a function of the model parameters. This enables us to deal with the energetics of the model and evaluate either its efficiency or its coefficient of performance depending upon whether the model functions either as a heat engine or as a refrigerator, respectively. We also study the way current changes with changes in parameters…
A microscopic heat engine is modeled as a Brownian particle in a sawtooh potential (with load) moving through a highly viscous medium driven by the thermal kick it gets from alternately placed hot and cold heat reservoirs. We found closed form expression for the current as a function of the parameters characterizing the model. Depending on the values these model parameters take, the engine is also found to function as a refrigerator. Expressions for the efficiency as well as for the refrigerator performance are also reported. Study of how these quantities depend on the model parameters enabled…
The thermodynamic uncertainty relation, originally derived for classical Markov-jump processes, provides a trade-off relation between precision and dissipation, deepening our understanding of the performance of quantum thermal machines. Here, we examine the interplay of quantum system coherences and heat current fluctuations on the validity of the thermodynamics uncertainty relation in the quantum regime. To achieve the current statistics, we perform a full counting statistics simulation of the Redfield quantum master equation. We focus on steady-state quantum absorption refrigerators where no…
We study the performance of a three-terminal thermoelectric device such as heat engine and refrigerator with broken time-reversal symmetry by applying the unified trade-off figure of merit ($\dotΩ$ criterion) which accounts for both useful energy and losses. For heat engine, we find that a thermoelectric device working under the maximum $\dotΩ$ criterion gives a significantly better performance than a device working at maximum power output. Within the framework of linear irreversible thermodynamics such a direct comparison is not possible for refrigerators, however, our study indicates that, f…
We analytically derive maximum efficiency at given cooling power for Carnot-type low-dissipation refrigerators. The corresponding optimal cycle duration depends on a single parameter, which is a specific combination of irreversibility parameters and bath temperatures. For a slight decrease in power with respect to its maximum value, the maximum efficiency exhibits an infinitely-fast nonlinear increase, which is standard in heat engines, only for a limited range of parameters. Otherwise, it increases only linearly with the slope given by ratio of irreversibility parameters. This behavior can be…
We study the coefficient of performance (COP) and its bounds of the Canot-like refrigerator working between two heat reservoirs at constant temperatures $T_h$ and $T_c$, under two optimization criteria $χ$ and $Ω$. In view of the fact that an "adiabatic" process takes finite time and is nonisentropic, the nonadiabatic dissipation and the finite time required for the "adiabatic" processes are taken into account. For given optimization criteria, we find that the lower and upper bounds of the COP are the same as the corresponding ones obtained from the previous idealized models where any adiabati…
We investigate generic heat engines and refrigerators operating between two heat reservoirs, for the condition when their efficiencies are equal to each other. It is shown that the corresponding value of efficiency is given as the inverse of the generalized golden mean, $ϕ_p$, where the parameter $p$ depends on the degree of irreversibility of both engine and refrigerator. The reversible case ($p=1$) yields the efficiency in terms of the standard golden mean. We also extend the analysis to a three-heat-resrervoir setup.
We analyze the performance of slowly driven meso- and micro-scale refrigerators and heat engines that operate between two thermal baths with small temperature difference. Using a general scaling argument, we show that such devices can work arbitrarily close to their Carnot limit only if heat-leaks between the baths are fully suppressed. Their power output is then subject to a universal geometric bound that decays quadratically to zero at the Carnot limit. This bound can be asymptotically saturated in the quasi-static limit if the driving protocols are suitably optimized and the temperature dif…
Thermodynamics is a branch of science blessed by an unparalleled combination of generality of scope and formal simplicity. Based on few natural assumptions together with the four laws, it sets the boundaries between possible and impossible in macroscopic aggregates of matter. This triggered groundbreaking achievements in physics, chemistry and engineering over the last two centuries. Close analogues of those fundamental laws are now being established at the level of individual quantum systems, thus placing limits on the operation of quantum-mechanical devices. Here we study quantum absorption …
We study universal aspects of fluctuations in an ensemble of noninteracting continuous quantum thermal machines in the steady state limit. Considering an individual machine, such as a refrigerator, in which relative fluctuations (and high order cumulants) of the cooling heat current to the absorbed heat current, $η^{(n)}$, are upper-bounded, $η^{(n)}\leq η_C^n$ with $n\geq 2$ and $η_C$ the Carnot efficiency, we prove that an {\it ensemble} of $N$ distinct machines similarly satisfies this upper bound on the relative fluctuations of the ensemble, $η_N^{(n)}\leq η_C^n$. For an ensemble of distin…
We demonstrate that a quantum absorption refrigerator can be realized from the smallest quantum system, a qubit, by coupling it in a non-additive (strong) manner to three heat baths. This function is un-attainable for the qubit model under the weak system-bath coupling limit, when the dissipation is additive. In an optimal design, the reservoirs are engineered and characterized by a single frequency component. We obtain then closed expressions for the cooling window and refrigeration efficiency, as well as bounds for the maximal cooling efficiency and the efficiency at maximal power. Our resul…
A two-level atomic system as a working substance is used to set up a refrigerator consisting of two quantum adiabatic and two isochoric processes (two constant-frequency processes $ω_a$ and $ω_b$ with $ω_a<ω_b$), during which the two-level system is in contact with two heat reservoirs at temperatures $T_h$ and $T_c (<T_h)$. Considering finite-time operation of two isochoric processes, we derive analytical expressions for cooling rate $R$ and coefficient of performance (COP) $\varepsilon$. The COP at maximum $χ(= \varepsilon R)$ figure of merit is numerically determined, and it is proved to be …
We derive cooling rate and coefficient of performance as well as their variances for a quantum Otto engine proceeding in finite-time cycle period. This machine consists of two driven strokes, where the system isolated from the heat reservoir undergoes finite-time unitary transformation, and two isochoric steps, where the finite-time system-bath interaction durations take the system away from the equilibrium even at the respective ends of the two stages. We explicitly calculate the statistics of cooling rate and coefficient of performance for the machine operating with an analytically solvable …
Motivated by the recent work by Mandal and Jarzynski on autonomous Maxwell demon information engine, we have extended their model by introducing two different heat baths. The system (demon) is coupled to a memory register (tape) and a work source. The performance of the system depends on the interplay between these two sources along with the heat baths. We have found the system can act as an engine, refrigerator or an eraser. Even the combination of any two is possible in some parameter space. We have achieved the efficiency of the engine is greater than Carnot limit. The coefficient of perfor…
We revisit the model of a Brownian particle in a heat bath submitted to an actively controlled force proportional to the velocity that leads to thermal noise reduction (cold damping). We investigate the influence of the continuous feedback on the fluctuations of the total entropy production and show that the explicit expression of the detailed fluctuation theorem involves different dynamics and observables in the forward and backward processes. As an illustration, we study the analytically solvable case of a harmonic oscillator and calculate the characteristic function of the entropy productio…
We present results obtained by using nonlinear irreversible models for heat devices. In particular, we focus on the global performance characteristics, the maximum efficiency and the efficiency at maximum power regimes for heat engines, and the maximum coefficient of performance (COP) and the COP at maximum cooling power regimes for refrigerators. We analyze the key role played by the interplay between irreversibilities coming from heat leaks and internal dissipations. We also discuss the relationship between these results and those obtained by different models.
Quantum heat cycles and quantum refrigerators are analyzed using various quantum systems as their working mediums. For example, to evaluate the efficiency and the work done of the Carnot cycle in the quantum regime, one can consider the harmonic oscillator as it's working medium. For all these well-defined working substances (which are analyzed in commutative space structure), the efficiency of the engine is not up to the mark of the Carnot efficiency. So, one inevitable question arise, can one observe a catalytic effect on the efficiency of the engines and refrigerators when the space structu…
We review theoretical approaches to analyzing efficiency of steady state heat to work conversion which is crucial in the timely problem of optimizing efficiency of small-scale heat engines and refrigerators. A rather abstract perspective of non-equilibrium statistical mechanics and dynamical system's theory is taken to view at this very practical problem. Several recently discovered general mechanisms of optimizing the figure of merit of thermoelectric efficiency are discussed, also in connection to breaking time-reversal symmetry of the microscopic equations of motion. Applications of these t…
While Carnot's model engines demonstrate ideal performances regarding conversion efficiency, they cannot be actually used as energy converters since they are non causal systems. Such an unphysical behavior indeed restrains the working conditions to a single point where, in the case of a refrigerator (generator), the cooling power (output power) vanishes. Focusing on the example of a thermoelectric refrigerator, we study the impact of different dissipation sources on the causality of such systems. Basing our analysis on the block diagram description of this system, we discuss particularly the f…
