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We characterize finite-time thermodynamic processes of multidimensional quadratic overdamped systems. Analytic expressions are provided for heat, work, and dissipation for any evolution of the system covariance matrix. The Bures-Wasserstein metric between covariance matrices naturally emerges as the local quantifier of dissipation. General principles of how to apply these geometric tools to identify optimal protocols are discussed. Focusing on the relevant slow-driving limit, we show how these results can be used to analyze cases in which the experimental control over the system is partial., Comment: Comments are welcome!

We optimize finite-time stochastic heat engines with a periodically scaled Hamiltonian under experimentally motivated constraints on the bath temperature $T$ and the scaling parameter $\lambda$. We present a general geometric proof that maximum-efficiency protocols for $T$ and $\lambda$ are piecewise constant, alternating between the maximum and minimum allowed values. When $\lambda$ is restricted to a small range and the system is close to equilibrium at the ends of the isotherms, a similar argument shows that this protocol also maximizes output power. These results are valid for arbitrary dynamics. We illustrate them for an overdamped Brownian heat engine, which can experimentally be realized using optical tweezers with stiffness $\lambda$., Comment: 13 pages, 7 figures

We derive an analytical expression for maximum efficiency at fixed power of heat pumps operating along a finite-time reverse Carnot cycle under the low-dissipation assumption. The result is cumbersome, but it implies simple formulas for tight upper and lower bounds on the maximum efficiency and various analytically tractable approximations. In general, our results qualitatively agree with those obtained earlier for endoreversible heat pumps. In fact, we identify a special parameter regime when the performance of the low-dissipation and endoreversible devices is the same. At maximum power, heat pumps operate as work to heat converters with efficiency 1. Expressions for maximum efficiency at given power can be helpful in the identification of more practical operation regimes.

We consider absorption refrigerators consisting of simultaneously operating Carnot-type heat engine and refrigerator. Their maximum efficiency at given power (MEGP) is given by the product of MEGPs for the internal engine and refrigerator. The only subtlety of the derivation lies in the fact that the maximum cooling power of the absorption refrigerator is not limited just by the maximum power of the internal refrigerator but, due to the first law, also by that of the internal engine. As a specific example, we consider the simultaneous absorption refrigerators composed of low-dissipation (LD) heat engines and refrigerators, for which the expressions for MEGPs are known. The derived expression for maximum efficiency implies bounds on the MEGP of LD absorption refrigerators. It also implies that a slight decrease in power of the absorption refrigerator from its maximum value results in a large nonlinear increase in efficiency observed in heat engines whenever the ratio of maximum powers of the internal engine and the refrigerator does not diverge. Otherwise, the increase in efficiency is linear as observed in LD refrigerators. Thus, in all practical situations, the efficiency of LD absorption refrigerators significantly increases when their cooling power is slightly decreased from its maximum.

We analytically derive maximum efficiency at given cooling power for Carnot-type low-dissipation refrigerators. The corresponding optimal cycle duration depends on a single parameter, which is a specific combination of irreversibility parameters and bath temperatures. For a slight decrease in power with respect to its maximum value, the maximum efficiency exhibits an infinitely-fast nonlinear increase, which is standard in heat engines, only for a limited range of parameters. Otherwise, it increases only linearly with the slope given by ratio of irreversibility parameters. This behavior can be traced to the fact that maximum power is attained for vanishing duration of the hot isotherm. Due to the lengthiness of the full solution for the maximum efficiency, we discuss and demonstrate these results using simple approximations valid for parameters yielding the two different qualitative behaviors. We also discuss relation of our findings to those obtained for minimally nonlinear irreversible refrigerators., Comment: 10 pages, 4 figures, updated references