According to the laws of thermodynamics, no heat engine can beat the efficiency of a Carnot cycle. This efficiency traditionally comes with vanishing power output and practical designs, optimized for power, generally achieve far less. Recently, various strategies to obtain Carnot's efficiency at large power were proposed. However, a thermodynamic uncertainty relation implies that steady-state heat engines can operate in this regime only at the cost of large fluctuations that render them immensely unreliable. Here, we demonstrate that this unfortunate trade-off can be overcome by designs operating cyclically under quasi-static conditions. The experimentally relevant yet exactly solvable model of an overdamped Brownian heat engine is used to illustrate the formal result. Our study highlights that work in cyclic heat engines and that in quasi-static ones are different stochastic processes.

Self-organization is the generation of order out of local interactions. It is deeply connected to many fields of science from physics, chemistry to biology, all based on physical interactions. The emergence of collective animal behavior is the result of self-organization processes as well, though they involve abstract interactions arising from sensory inputs, information processing, storage, and feedback. Resulting collective behaviors are found, for example, in crowds of people, flocks of birds, and swarms of bacteria. Here we introduce interactions between active microparticles which are based on the information about other particle positions. A real-time feedback of multiple active particle positions is the information source for the propulsion direction of these particles. The emerging structures require continuous information flows. They reveal frustrated geometries due to confinement to two dimensions and internal dynamical degrees of freedom that are reminiscent of physically bound systems, though they exist only as nonequilibrium structures.

We investigate a stochastic heat engine based on an over-damped particle diffusing on the positive real axis in an externally driven time-periodic log-harmonic potential. The periodic driving is composed of two isothermal and two adiabatic branches. Within our specific setting we verify the recent universal results regarding efficiency at maximum power and discuss properties of the optimal protocol. Namely, we show that for certain fixed parameters the optimal protocol maximizes not only the output power but also the efficiency. Moreover, we calculate the variance of the output work and discuss the possibility to minimize fluctuations of the output power.PACS numbers: 05.70.Ln, 07.20.Pe ‡ It turns out that for general parameters g ± the Green's function (11) is given by a sum of Gauss hypergeometric functions [21] and the integral Eq. (4) becomes quite complicated.