Success versus failure: Efficient heat devices in thermodynamics

Classical equilibrium thermodynamics provides, in a general way, upper Carnot bounds for the performance of energy converters. Nevertheless, to suggest lower bounds is a much more subtle issue, especially when they are related to a definition of convenience. Here, this issue is investigated in a unified way for heat engines, refrigerators, and heat pumps. First, irreversibilities are weighted in the context of heat reservoir stability for irreversible engines by using the thermodynamic distance between minimum energy and maximum entropy steady states. Some stability coefficients can be related to a majorization process and the obtention of Pareto fronts, linking stability and optimization by means of efficiency and entropy due to correlations between system and reservoirs. Second, these findings are interpreted in a very simple context. A region where the heat device is efficient is defined in a general scheme and, below this zone, the heat device is inefficient in the sense that irreversibilities somehow dominate its behavior. These findings allow for a clearer understanding of the role played by some well-known figures of merit in the scope of finite-time and -size optimization. Comparison with experimental results is provided.

Thermodynamic optimization subsumed in stability phenomena

In the present paper the possibility of an energetic self-optimization as a consequence of thermodynamic stability is addressed. This feature is analyzed in a low dissipation refrigerator working in an optimized trade-off regime (the so-called Omega function). The relaxation after a perturbation around the stable point indicates that stability is linked to trajectories in which the thermodynamic performance is improved. Furthermore, a limited control over the system is analyzed through consecutive external random perturbations. The statistics over many cycles corroborates the preference for a better thermodynamic performance. Endoreversible and irreversible behaviors play a relevant role in the relaxation trajectories (as well as in the statistical performance of many cycles experiencing random perturbations). A multi-objective optimization reveals that the well-known endoreversible limit works as an attractor of the system evolution coinciding with the Pareto front, which represents the best energetic compromise among efficiency, entropy generation, cooling power, input power and the Omega function. Meanwhile, near the stable state, performance and stability are dominated by an irreversible behavior.

Energetic Self-Optimization Induced by Stability in Low-Dissipation Heat Engines

The local stability of a weakly dissipative heat engine is analyzed and linked to an energetic multi-objective optimization perspective. This constitutes a novel issue in the unified study of cyclic energy converters, opening the perspective to the possibility that stability favors self-optimization of thermodynamic quantities including efficiency, power and entropy generation. To this end, a dynamics simulating the restitution forces, which mimics a harmonic potential, bringing the system back to the steady state is analyzed. It is shown that relaxation trajectories are not arbitrary but driven by the improvement of several energetic functions. Insights provided by the statistical behavior of consecutive random perturbations show that the irreversible behavior works as an attractor for the energetics of the system, while the endoreversible limit acts as an upper bound and the Pareto front as a global attractor. Fluctuations around the operation regime reveal a difference between the behavior coming from fast and slow relaxation trajectories: while the former are associated to an energetic self-optimization evolution, the latter are ascribed to better performances. The self-optimization induced by stability and the possible use of instabilities in the operation regime to improve the energetic performance might usher into new useful perspectives in the control of variables for real engines.

Optimization induced by stability and the role of limited control near a steady state

A relationship between stability and self-optimization is found for weakly dissipative heat devices. The effect of limited control on operation variables around an steady state is such that, after instabilities, the paths toward relaxation are given by trajectories stemming from restitution forces which improve the system thermodynamic performance (power output, efficiency, and entropy generation). Statistics over random trajectories for many cycles shows this behavior as well. Two types of dynamics are analyzed, one where an stability basin appears and another one where the system is globally stable. Under both dynamics there is an induced trend in the control variables space due to stability. In the energetic space this behavior translates into a preference for better thermodynamic states, and thus stability could favor self-optimization under limited control. This is analyzed from the multiobjective optimization perspective. As a result, the statistical behavior of the system is strongly influenced by the Pareto front (the set of points with the best compromise between several objective functions) and the stability basin. Additionally, endoreversible and irreversible behaviors appear as very relevant limits: The first one is an upper bound in energetic performance, connected with the Pareto front, and the second one represents an attractor for the stochastic trajectories.

Entropy generation and unified optimization of Carnot-like and low-dissipation refrigerators

The connection between Carnot-like and low-dissipation refrigerators is proposed by means of their entropy generation and the optimization of two unified, compromise-based figures of merit. Their optimization shows that only a limited set of heat transfer laws in the Carnot-like model are compatible with the results stemming from the low-dissipation approximation, even though there is an agreement of the related physical spaces of variables. A comparison between two operation regimes and relations among entropy generation, efficiency, cooling power. and power input are obtained, with emphasis on the role of dissipation symmetries. The results extend previous findings for heat engines at maximum power conditions.

From maximum power to a trade-off optimization of low-dissipation heat engines: Influence of control parameters and the role of entropy generation

For a low-dissipation heat engine model we present the role of the partial contact times and the total operational time as control parameters to switch from maximum power state to maximum Ω trade-off state. The symmetry of the dissipation coefficients may be used in the design of the heat engine to offer, in such switching, a suitable compromise between efficiency gain, power losses, and entropy change. Bounds for entropy production, efficiency, and power output are presented for transitions between both regimes. In the maximum power and maximum Ω trade-off cases the relevant space of parameters are analyzed together with the configuration of minimum entropy production. A detailed analysis of the parameter's space shows physically prohibited regions in which there is no longer a heat engine and another region that is physically well behaved but is not suitable for possible optimization criteria.

Heat devices in nonlinear irreversible thermodynamics

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.

Coefficient of performance for a low-dissipation Carnot-like refrigerator with nonadiabatic dissipation

We study the coefficient of performance (COP) and its bounds for a Carnot-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 usually takes finite time and is nonisentropic, the nonadiabatic dissipation and the finite time required for the adiabatic processes are taken into account by assuming low dissipation. 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 adiabatic process is undergone instantaneously with constant entropy. To describe some particular models with very fast adiabatic transitions, we also consider the influence of the nonadiabatic dissipation on the bounds of the COP, under the assumption that the irreversible entropy production in the adiabatic process is constant and independent of time. Our theoretical predictions match the observed COPs of real refrigerators more closely than the ones derived in the previous models, providing a strong argument in favor of our approach.

Low-dissipation heat devices: unified trade-off optimization and bounds

We apply a unified and trade-off based optimization for low-dissipation models of cyclic heat devices which accounts for both useful energy and losses. The resulting performance regime lies between those of maximum first-law efficiency and maximum χ (a unified figure of merit corresponding to power output of heat engines). The bounds available for both symmetric and extremely asymmetric heat devices are explicitly obtained. The similarities for heat engines and refrigerators and the energetic advantages of the trade-off optimization are especially stressed.

Coefficient of performance at maximum figure of merit and its bounds for low-dissipation Carnot-like refrigerators

The figure of merit for refrigerators performing finite-time Carnot-like cycles between two reservoirs at temperature T(h) and T(c) (<T(h)) is optimized. It is found that the coefficient of performance at maximum figure of merit is bounded between 0 and (sqrt[9+8ε(c)] - 3)/2 for the low-dissipation refrigerators, where ε(c) = T(c)/(T(h) - T(c)) is the Carnot coefficient of performance for reversible refrigerators. These bounds can be reached for extremely asymmetric low-dissipation cases when the ratio between the dissipation constants of the processes in contact with the cold and hot reservoirs approaches to zero or infinity, respectively. The observed coefficients of performance for real refrigerators are located in the region between the lower and upper bounds, which is in good agreement with our theoretical estimation.

Optimal low symmetric dissipation Carnot engines and refrigerators

A unified optimization criterion for Carnot engines and refrigerators is proposed. It consists of maximizing the product of the heat absorbed by the working system times the efficiency per unit time of the device, either the engine or the refrigerator. This criterion can be applied to both low symmetric dissipation Carnot engines and refrigerators. For engines the criterion coincides with the maximum power criterion and then the Curzon-Ahlborn efficiency η(CA)=1-√T(c)/T(h) is recovered, where T(h) and T(c) are the temperatures of the hot and cold reservoirs, respectively [Esposito, Kawai, Lindenberg, and Van den Broeck, Phys. Rev. Lett. 105, 150603 (2010)]. For refrigerators the criterion provides the counterpart of Curzon-Ahlborn efficiency for refrigerators ε(CA)=[1/(√1-(T(c)/T(h))]-1, first derived by Yan and Chen for the particular case of an endoreversible Carnot-type refrigerator with linear (Newtonian) finite heat transfer laws [Yan and Chen, J. Phys. D: Appl. Phys. 23, 136 (1990)].

Dynamical characterization of rotationally hindered species in liquids

The rotational dynamics of HCl in liquid Ar has been studied by means of molecular-dynamics simulations. We calculate the lifetimes of weakly bound HCl-Ar dimers induced by the anisotropic pair interaction. It is shown that, although lifetimes are small with respect to the reorientational decorrelation, the time interval between the breaking down and formation of the next dimer is negligibly small. Thus, with respect to the rotational dynamics of the probe, the effect is similar to that and eventually would cause a time-stable complex. This provokes a peculiar hindered rotation of the diatomic in the liquid which is macroscopically embodied in the infrared spectrum of the solution as a Q-branch nonexistent otherwise.

Infrared spectral profiles in liquids and atom-diatom interactions

Molecular dynamics simulations of the infrared spectrum of a generic simple polar diatomic in a liquid nonpolar solvent allow to reproduce the different prototypical experimental line shapes of this kind of systems. This is feasible by using different solute-solvent anisotropic potentials at fixed thermodynamic conditions. In the limit cases, the rotation of the diatomic is explained in terms of a quasifree motion or a rotational diffusion evolution and the spectra show a doublet structure formed by P and R branches or a unique collapsed branch, respectively. When the profile contains three branches, including an intense Q branch in the vicinity of the center of the band, rotational evolution presents a particular hindering that can be understood by studying the influence on rotational spectral densities of the different time scales involved in rotational relaxation. Cancellation/enhancement effects among spectral density terms arising from intermediate and long times (0.4-1 ps) are essential to understand rotational hindering.