Karel Proesmans

Onsager Coefficients in Periodically Driven Systems.

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.

Discrete-time thermodynamic uncertainty relation

We generalize the thermodynamic uncertainty relation, providing an entropic upper bound for average fluxes in time-continuous steady-state systems (Gingrich et al., Phys. Rev. Lett. 116, 120601 (2016)), to time-discrete Markov chains and to systems under time-symmetric, periodic driving.

Power-Efficiency-Dissipation Relations in Linear Thermodynamics.

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.

Linear stochastic thermodynamics for periodically driven systems

The theory of linear stochastic thermodynamics is developed for periodically driven systems in contact with a single reservoir. 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.

Brownian Duet: A Novel Tale of Thermodynamic Efficiency

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 these results are experimentally tested without adjustable parameters on a colloidal system.

Stochastic efficiency: five case studies

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.

The underdamped Brownian duet and stochastic linear irreversible thermodynamics

Building on our earlier work [Proesmans et al., Phys. Rev. X 6, 041010 (2016)], we introduce the underdamped Brownian duet as a prototype model of a dissipative system or of a work-to-work engine. Several recent advances from the theory of stochastic thermodynamics are illustrated with explicit analytic calculations and corresponding Langevin simulations. In particular, we discuss the Onsager-Casimir symmetry, the trade-off relations between power, efficiency and dissipation, and stochastic efficiency.

Efficiency of single-particle engines.

We study the efficiency of a single-particle Szilard and Carnot engine. Within a first order correction to the quasistatic limit, the work distribution is found to be Gaussian and the correction factor to average work and efficiency only depends on the piston speed. The stochastic efficiency is studied for both models and the recent findings on efficiency fluctuations are confirmed numerically. Special features are revealed in the zero-temperature limit.