Thermodynamics in finite time

Abstract

Until the 19th century, technology was essentially the domain of skilled artisans and constructors who relied on practical experience to design and build their machines. One of the first efforts to use physical theory to study the functioning of machines was undertaken by the French engineer Sadi Carnot. Motivated by the concern of the French about the superiority of British steam engines, he undertook a systematic study of the physical processes governing steam engines, resulting in his remarkable paper Reflexions sur la puissance motrice du feu (On the Motive Power of Heat) published in 1826. Among the earliest successes of this new science, thermodynamics, was the formulation of criteria describing how well real processes perform in comparison with an ideal model. Carnot showed that any engine, using heat from a hot reservoir at temperature Th to do work, has to transfer some heat to a reservoir at lower temperature T1, and that no engine could convert into work more of the heat taken in at Th than the fraction ηC = 1−(T1/Th) known as the Carnot efficiency.

Principles of control thermodynamics

“…For this reason, Michel Feidt advocated calling this body of work finite-resource thermodynamics. 11 While this argument has some validity, we believe that the role of time is special and deserves to be singled out. Nevertheless, we adopt the name control thermodynamics to describe these results.…”

“…One of the early findings of the Berry group was the existence of a number of interesting objective functions for thermodynamic processes in finite time [11]. In particular, two interesting optimal strategies represented the polar extremes of the go-all-out strategy versus the save-fortomorrow strategy.…”

Thermodynamic R-diagrams reveal solid-like fluid states

“…A pioneering paper on this was by Weinhold [1] who introduced a thermodynamic energy inner product. This led to the work of Ruppeiner [2] who wrote a Riemannian thermodynamic entropy metric to represent thermodynamic fluctuation theory, and was the first to systematically calculate the thermodynamic Ricci curvature scalar R. A parallel effort was by Andresen, Salamon, and Berry [3] who began the systematic application of the thermodynamic entropy metric to finite-time thermodynamic processes.…”

Time-dependent, irreversible entropy production and geodynamics

“…Therefore, we hope to be able to extend the yield design theory underpinned by the limit theorems in continuum mechanics (Salencon 2002) for discrete examples in the future. Also, if we assume the temperature of the environment T surf to be constant, we can use an explicit open system formulation and from integrating equation (5.3) over finite time we recover the basic equation for finite-time thermodynamics (Andresen et al 1984). Note that the analogy of the limit theorems in terms of work can only be cast rigorously into a limit theorem of dissipated power and not integrated for work.…”