Efficiency at maximum power: An analytically solvable model for stochastic heat engines

We study a class of cyclic Brownian heat engines in the framework of finite-time thermodynamics. For infinitely long cycle times, the engine works at the Carnot efficiency limit producing, however, zero power. For the efficiency at maximum power, we find a universal expression, different from the endoreversible Curzon-Ahlborn efficiency. Our results are illustrated with a simple one-dimensional engine working in and with a time-dependent harmonic potential.Comment: 6 pages, 3 figure

Interaction of molecular motors can enhance their efficiency

Particles moving in oscillating potential with broken mirror symmetry are considered. We calculate their energetic efficiency, when acting as molecular motors carrying a load against external force. It is shown that interaction between particles enhances the efficiency in wide range of parameters. Possible consequences for artificial molecular motors are discussed.Comment: 6 pages, 8 figure

A minimal model of an autonomous thermal motor

We consider a model of a Brownian motor composed of two coupled overdamped degrees of freedom moving in periodic potentials and driven by two heat reservoirs. This model exhibits a spontaneous breaking of symmetry and gives rise to directed transport in the case of a non- vanishing interparticle interaction strength. For strong coupling between the particles we derive an expression for the propagation velocity valid for arbitrary periodic potentials. In the limit of strong coupling the model is equivalent to the B\"uttiker-Landauer model [1-3] for a single particle diffusing in an environment with position dependent temperature. By using numerical calculations of the Fokker-Planck equation and simulations of the Langevin equations we study the model for arbitrary coupling, retrieving many features of the strong coupling limit. In particular, directed transport emerges even for symmetric potentials. For distinct heat reservoirs the heat currents are well-defined quantities allowing a study of the motor efficiency. We show that the optimal working regime occurs for moderate coupling. Finally, we introduce a model with discrete phase space which captures the essential features of the continuous model, can be solved in the limit of weak coupling, and exhibits a larger efficiency than the continuous counterpart.Comment: Revised version. Extended discussion on the discrete model. To appear in EP

Efficiency of Free Energy Transduction in Autonomous Systems

We consider the thermodynamics of chemical coupling from the viewpoint of free energy transduction efficiency. In contrast to an external parameter-driven stochastic energetics setup, the dynamic change of the equilibrium distribution induced by chemical coupling, adopted, for example, in biological systems, is inevitably an autonomous process. We found that the efficiency is bounded by the ratio between the non-symmetric and the symmetrized Kullback-Leibler distance, which is significantly lower than unity. Consequences of this low efficiency are demonstrated in the simple two-state case, which serves as an important minimal model for studying the energetics of biomolecules.Comment: 4 pages, 4 figure

Bounds of efficiency at maximum power for linear, superlinear and sublinear irreversible Carnot-like heat engines

The efficiency at maximum power (EMP) of irreversible Carnot-like heat engines is investigated based on the weak endoreversible assumption and the phenomenologically irreversible thermodynamics. It is found that the weak endoreversible assumption can reduce to the conventional one for the heat engines working at maximum power. Carnot-like heat engines are classified into three types (linear, superlinear, and sublinear) according to different characteristics of constitutive relations between the heat transfer rate and the thermodynamic force. The EMPs of Carnot-like heat engines are proved to be bounded between $\eta_C/2$ and $\eta_C/(2-\eta_C)$ for the linear type, 0 and $\eta_C/(2-\eta_C)$ for the superlinear type, and $\eta_C/2$ and $\eta_C$ for the sublinear type, respectively, where $\eta_C$ is the Carnot efficiency.Comment: 6 journal pages, 1 figure, EPL (in press

Heat release by controlled continuous-time Markov jump processes

We derive the equations governing the protocols minimizing the heat released by a continuous-time Markov jump process on a one-dimensional countable state space during a transition between assigned initial and final probability distributions in a finite time horizon. In particular, we identify the hypotheses on the transition rates under which the optimal control strategy and the probability distribution of the Markov jump problem obey a system of differential equations of Hamilton-Bellman-Jacobi-type. As the state-space mesh tends to zero, these equations converge to those satisfied by the diffusion process minimizing the heat released in the Langevin formulation of the same problem. We also show that in full analogy with the continuum case, heat minimization is equivalent to entropy production minimization. Thus, our results may be interpreted as a refined version of the second law of thermodynamics.Comment: final version, section 2.1 revised, 26 pages, 3 figure