We derive general relations between the maximum power, maximum efficiency, and minimum dissipation regimes from linear irreversible thermodynamics. The relations simplify further in the presence of a particular symmetry of the Onsager matrix, which can be derived from detailed balance. The results are illustrated on a periodically driven system and a three-terminal device subject to an external magnetic field.

We evaluate the Onsager matrix for a system under time-periodic driving by considering all its Fourier components. By application of the second law, we prove that all the fluxes converge to zero in the limit of zero dissipation. Reversible efficiency can never be reached at finite power. The implication for an Onsager matrix, describing reduced fluxes, is that its determinant has to vanish. In the particular case of only two fluxes, the corresponding Onsager matrix becomes symmetric.

We calculate analytically the stochastic thermodynamic properties of an isothermal Brownian engine driven by a duo of time-periodic forces, including its Onsager coefficients, the stochastic work of each force, and the corresponding stochastic entropy production. We verify the relations between different operational regimes, maximum power, maximum efficiency, and minimum dissipation, and reproduce the signature features of the stochastic efficiency. All of these results are experimentally tested without adjustable parameters on a colloidal system.

Active constituents burn fuel to sustain individual motion, giving rise to collective effects that are not seen in systems at thermal equilibrium, such as phase separation with purely repulsive interactions. There is a great potential in harnessing the striking phenomenology of active matter to build novel controllable and responsive materials that surpass passive ones. Yet, we currently lack a systematic roadmap to predict the protocols driving active systems between different states in a way that is thermodynamically optimal. Equilibrium thermodynamics is an inadequate foundation to this end, due to the dissipation rate arising from the constant fuel consumption in active matter. Here, we derive and implement a versatile framework for the thermodynamic control of active matter. Combining recent developments in stochastic thermodynamics and response theory, our approach shows how to find the optimal control for either continuous- or discrete-state active systems operating out of equilibrium. Our results open the door to designing novel active materials that are not only built to stabilize specific nonequilibrium collective states but are also optimized to switch between different states at minimum dissipation. Published by the American Physical Society 2024

We develop a theory of linear stochastic thermodynamics for general periodically driven, Markovian systems. Appropriate thermodynamic forces and fluxes are identified, starting from the entropy production for a Markov process. Onsager coefficients are evaluated, the Onsager–Casimir relations are verified, and explicit expressions are given for an expansion in terms of Fourier components. The results are illustrated on a periodically modulated two level system including the optimization of the power output.

Stochastic efficiency is evaluated in five case studies: driven Brownian motion, effusion with a thermo-chemical and thermo-velocity gradient, a quantum dot and a model for information to work conversion. The salient features of stochastic efficiency, including the maximum of the large deviation function at the reversible efficiency, are reproduced. The approach to and extrapolation into the asymptotic time regime are documented.