Degenerate optimal paths in thermally isolated systems

Abstract

We present an analysis of the work performed on a system of interest that is kept thermally isolated during the switching of a control parameter. We show that there exists, for a certain class of systems, a finite-time family of switching protocols for which the work is equal to the quasistatic value. These optimal paths are obtained within linear response for systems initially prepared in a canonical distribution. According to our approach, such protocols are composed of a linear part plus a function which is odd with respect to time reversal. For systems with one degree of freedom, we claim that these optimal paths may also lead to the conservation of the corresponding adiabatic invariant. This points to an interesting connection between work and the conservation of the volume enclosed by the energy shell. To illustrate our findings, we solve analytically the harmonic oscillator and present numerical results for certain anharmonic examples.

Compatibility of linear-response theory with the second law of thermodynamics and the emergence of negative entropy production rates

“…[38]). In the last decades, expressions for W irr have been derived using linear-response theory for the purpose of finding optimal finite-time processes [39][40][41][42][43][44]. The connection between linear-response theory and the Second Law can be established then through these expressions for W irr which are asked to verify the following statements: 1.…”

“…In this regime, the relative change δλ/λ 0 must be small but the duration τ of the process can be arbitrary. In this case, using linear-response theory, the irreversible work expression reads [43]…”

“…For more details, see Refs. [42,43]. It is worth emphasizing that W irr is an average over several microscopic realizations of the protocol λ(t), each one furnishing a different value of work W. Hence, W irr ≡ W − ∆F is a fluctuating quantity that obeys very well-known fluctuation theorems, namely, the Jarzynski equality [45] e −β(W−∆F ) = e −βWirr = 1 ,…”

Microcanonical Szilárd engines beyond the quasistatic regime

“…This process is such that the average work W is equal to the negative of the quasistatic work W qs obtained in step 1 plus the excess work W ex (see, for instance, Ref. [36] for a discussion about W ex ). The protocol and switching time τ 2 are such that W ex < 0 (see Fig.…”

Speeding up a quantum refrigerator via counterdiabatic driving

“…In particular, the counter-diabatic driving (CD) technique [21][22][23][24][25][26] realizes STA by introducing an additional control field which enforces the system to follow the quantum adiabatic trajectory of the uncontrolled system. By utilizing these techniques, the performance of superadiabatic quantum heat engines have been studied extensively [27][28][29][30][31], whereas other optimization techniques have been utilized in the literature as well [32][33][34]. Note that the CD has been implemented in several experiments [35][36][37][38].…”