Universality of efficiency at unified trade-off optimization

Abstract

We calculate the efficiency at the unified trade-off optimization criterion (the so-called maximum Ω criterion) representing a compromise between the useful energy and the lost energy of heat engines operating between two reservoirs at different temperatures and chemical potentials, and demonstrate that the linear coefficient 3/4 and quadratic coefficient 1/32 of the efficiency at maximum Ω are universal for heat engines under strong coupling and symmetry conditions. It is further proved that the conclusions obtained here also apply to the ecological optimization criterion.

Optimization and Stability of Heat Engines: The Role of Entropy Evolution

“…A distinctive feature is that the trajectories are more lined and with a narrower basin of attraction. Notice that, when comparing with the MP results, the MΩ regime implies smaller entropy production trajectories and higher efficiency, in agreement with the bounds accounted for Equations (9) and (10) for high asymmetries and Equations (11) and (12) for the symmetric case. Notice in Figure 2c,d the different scales in entropy and efficiency with respect to Figure 2a,b Therefore, all the above provides a firm basis to consider that stability could be linked to a compromise of performance among η, P,˙ ∆S, in what we can call a thermodynamic "self-improvement" in the process of relaxation, with the smallest possible fluctuations on the performance of the engine.…”

“…All these problems involve entropy production (∆S), heat waste, power output (P) and efficiency η [1,2]. Along with maximum power and maximum efficiency or minimum entropy production, compromise based figures of merit have been found very valuable in the optimization analysis of heat devices [3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19]. In this framework, the so-called Ω function, defined as Ω ≡ P gain − P loss , was proposed, offering useful insights since it represents a trade off between maximum power gain (P gain ≡ P − P min ) and minimum power loss (P loss ≡ P max − P), with respect to the minimum and maximum available power output for a heat engine.…”

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

“…Nowadays, the aim to uncover general aspects related to operation regimes, beyond specific models and heat transfer mechanisms, is an active field [33][34][35][36][37][38][39][40][41][42]. For this purpose, the analysis of the maximum power regime is the most developed one so far.…”

Thermoelectric energy converters under a trade-off figure of merit with broken time-reversal symmetry

“…The dot denotes the quantity per unit time for steady-state heat devices or the quantity divided by one cycle time for cyclic heat devices. Several models of heat devices were studied under the maximumΩ criterion [44,45,46,47,48,49,50,51,52,53,54] and found that the efficiency under the maximumΩ criterion, η(Ω max ), lies between the maximum efficiency and the efficiency at maximum power output i.e., η max > η(Ω max ) > η(P max ) [43]. The efficiency of a linear irreversible heat engine working at maximum power is bounded below half of the Carnot efficiency and reaches η C /2 under the tightcoupling condition.…”