Averaged Optimization and Finite-Time Thermodynamics

Abstract

The paper considers typical extremum problems that contain mean values of control variables or some functions of these variables. Relationships between such problems and cyclic modes of dynamical systems are explained and optimality conditions for these modes are found. The paper shows how these problems are linked to the field of finite-time thermodynamics.

Quantum Finite-Time Thermodynamics: Insight from a Single Qubit Engine

“…In fact, macroscopic optimizations of finite-time Carnot cycles [ 8 ] would lead to maximum energy exchange for a given entropy change of the working fluid and suggests that better use of the heat exchange time would be to utilize it fully by keeping the coherence for conversion during the following unitary stroke. Our expectation for an optimal implementation would be one that keeps the entropy production rate constant [ 139 , 140 ], and examining these rates in Figure 17 shows that our constant protocol comes reasonably close.…”

Modeling and Performance Optimization of an Irreversible Two-Stage Combined Thermal Brownian Heat Engine

“…FTT theory has been applied for performance optimization of various macro energy systems. The applications of FTT include many aspects and the two major aspects are optimal configurations [ 8 , 9 , 10 , 11 , 12 , 13 , 14 , 15 , 16 , 17 , 18 , 19 , 20 , 21 , 22 , 23 , 24 ] and optimal performances [ 25 , 26 , 27 , 28 , 29 , 30 , 31 , 32 , 33 , 34 , 35 , 36 , 37 , 38 , 39 , 40 , 41 , 42 , 43 , 44 , 45 , 46 , 47 , 48 , 49 , 50 , 51 , 52 , 53 , 54 , 55 , 56 , 57 , 58 , 59 , 60 , 61 , 62 ,…”

“…FTT theory has been applied for performance optimization of various macro energy systems. The applications of FTT include many aspects and the two major aspects are optimal configurations [8][9][10][11][12][13][14][15][16][17][18][19][20][21][22][23][24] and optimal performances studies.…”

Optimization Modeling of Irreversible Carnot Engine from the Perspective of Combining Finite Speed and Finite Time Analysis

“…However, regarding the usefulness of the FTT, the endoreversible model has the merit of launching nowadays the competition of finding new upper bounds of thermal machines performance, closer to the real one. Thus, progress has been made in the modeling and optimization of thermodynamic processes and cycles [ 24 , 25 , 26 , 27 , 28 , 29 , 30 , 31 , 32 ], with special attention to the common ones in thermal machines: Otto cycle [ 27 ], Stirling engine [ 28 ], Kalina cycle [ 30 ], and Brayton cycle [ 31 , 32 ]. The results obtained [ 30 , 31 ] have shown that besides the gains of FTT optimization with three or four objectives, the original results reported in the initial work of the FTT theory [ 3 , 4 , 5 ] are also revealed.…”