Approaching Carnot efficiency at maximum power in linear response regime

We construct an example of heat engine whose efficiency at maximum power breaks down the previously derived bounds in the linear response regime. Such example takes a classical harmonic oscillator as the working substance undergoing a finite-time Otto cycle. Using a specific kind of shortcut to adiabaticity, valid only in the linear response regime, quasistatic work is performed at arbitrarily short times. The cycle duration is then reduced to the sum of relaxation times during the thermalization strokes exclusively. Thus, power is maximum since the work is maximum (quasistatic work) and the cycle duration is minimum. Efficiency at maximum power can be made arbitrarily close to Carnot efficiency with an appropriate choice of the ratio between the temperatures of the two heat baths.Comment: 6 pages, 2 figure

Conditional reversibility in nonequilibrium stochastic systems

For discrete-state stochastic systems obeying Markovian dynamics, we establish the counterpart of the conditional reversibility theorem obtained by Gallavotti for deterministic systems [Ann. de l'Institut Henri Poincar\'e (A) 70, 429 (1999)]. Our result states that stochastic trajectories conditioned on opposite values of entropy production are related by time reversal, in the long-time limit. In other words, the probability of observing a particular sequence of events, given a long trajectory with a specified entropy production rate $\sigma$, is the same as the probability of observing the time-reversed sequence of events, given a trajectory conditioned on the opposite entropy production, $-\sigma$, where both trajectories are sampled from the same underlying Markov process. To obtain our result, we use an equivalence between conditioned ("microcanonical") and biased ("canonical") ensembles of nonequilibrium trajectories. We provide an example to illustrate our findings.Comment: 13 pages, 1 figur

Shortcuts to adiabaticity from linear response theory

A shortcut to adiabaticity is a finite-time process that produces the same final state as would result from infinitely slow driving. We show that such shortcuts can be found for weak perturbations from linear response theory. With the help of phenomenological response functions a simple expression for the excess work is found -- quantifying the nonequilibrium excitations. For two specific examples, the quantum parametric oscillator and the spin-1/2 in a time-dependent magnetic field, we show that finite-time zeros of the excess work indicate the existence of shortcuts. Finally, we propose a degenerate family of protocols, which facilitate shortcuts to adiabaticity for specific and very short driving times.Comment: 9 pages, 8 figure; published versio

Compatibility of linear-response theory with the Second Law of Thermodynamics and the emergence of negative entropy production rates

The reliability of physical theories depends on whether they agree with well established physical laws. In this work, we address the compatibility of the Hamiltonian formulation of linear-response theory with the Second Law of Thermodynamics. In order to do so, we verify three complementary aspects often understood as statements of the Second Law: 1. No dissipation for quasistatic process; 2. Dissipation for finite-time processes; 3. Positive entropy production rate. Our analysis focus on two classes of nonequilibrium isothermal processes: slowly-varying and finite-time but weak ones. For the former, we show that these aspects are easily verified. For the later, we present conditions for the achievement of the first two aspects. We also show that the third one is not always verified, presenting an example based on Brownian motion in which we observe negative values in the entropy production rate. In particular, we compare linear-response and exact results for this example.Comment: 11 pages, 7 figure

Thermodynamic control -- an old paradigm with new applications

Tremendous research efforts have been invested in exploring and designing so-called shortcuts to adiabaticity. These are finite-time processes that produce the same final states that would result from infinitely slow driving. Most of these techniques rely on auxiliary fields and quantum control techniques, which makes them rather costly to implement. In this Perspective we outline an alternative paradigm for optimal control that has proven powerful in a wide variety of situations ranging from heat engines over chemical reactions to quantum dynamics -- thermodynamic control. Focusing on only a few, selected milestones we seek to provide a pedagogical entry point into this powerful and versatile framework.Comment: 7 pages, 1 figure; Short review paper intended as Perspective in EPL (Europhys. Lett