Efficiency of autonomous soft nano-machines at maximum power

We consider nano-sized artificial or biological machines working in steady state enforced by imposing non-equilibrium concentrations of solutes or by applying external forces, torques or electric fields. For unicyclic and strongly coupled multicyclic machines, efficiency at maximum power is not bounded by the linear response value 1/2. For strong driving, it can even approach the thermodynamic limit 1. Quite generally, such machines fall in three different classes characterized, respectively, as "strong and efficient", "strong and inefficient", and "balanced". For weakly coupled multicyclic machines, efficiency at maximum power has lost any universality even in the linear response regime

Stochastic thermodynamics of chemical reaction networks

For chemical reaction networks described by a master equation, we define energy and entropy on a stochastic trajectory and develop a consistent nonequilibrium thermodynamic description along a single stochastic trajectory of reaction events. A first-law like energy balance relates internal energy, applied (chemical) work and dissipated heat for every single reaction. Entropy production along a single trajectory involves a sum over changes in the entropy of the network itself and the entropy of the medium. The latter is given by the exchanged heat identified through the first law. Total entropy production is constrained by an integral fluctuation theorem for networks arbitrarily driven by time-dependent rates and a detailed fluctuation theorem for networks in the steady state. Further exact relations like a generalized Jarzynski relation and a generalized Clausius inequality are discussed. We illustrate these results for a three-species cyclic reaction network which exhibits nonequilibrium steady states as well as transitions between different steady states.Comment: 14 pages, 2 figures, accepted for publication in J. Chem. Phy

Efficiency of a Brownian information machine

A Brownian information machine extracts work from a heat bath through a feedback process that exploits the information acquired in a measurement. For the paradigmatic case of a particle trapped in a harmonic potential, we determine how power and efficiency for two variants of such a machine operating cyclically depend on the cycle time and the precision of the positional measurements. Controlling only the center of the trap leads to a machine that has zero efficiency at maximum power whereas additional optimal control of the stiffness of the trap leads to an efficiency bounded between 1/2, which holds for maximum power, and 1 reached even for finite cycle time in the limit of perfect measurements.Comment: 9 pages, 2 figure

Hybrid simulations of lateral diffusion in fluctuating membranes

In this paper we introduce a novel method to simulate lateral diffusion of inclusions in a fluctuating membrane. The regarded systems are governed by two dynamic processes: the height fluctuations of the membrane and the diffusion of the inclusion along the membrane. While membrane fluctuations can be expressed in terms of a dynamic equation which follows from the Helfrich Hamiltonian, the dynamics of the diffusing particle is described by a Langevin or Smoluchowski equation. In the latter equations, the curvature of the surface needs to be accounted for, which makes particle diffusion a function of membrane fluctuations. In our scheme these coupled dynamic equations, the membrane equation and the Langevin equation for the particle, are numerically integrated to simulate diffusion in a membrane. The simulations are used to study the ratio of the diffusion coefficient projected on a flat plane and the intramembrane diffusion coefficient for the case of free diffusion. We compare our results with recent analytical results that employ a preaveraging approximation and analyze the validity of this approximation. A detailed simulation study of the relevant correlation functions reveals a surprisingly large range where the approximation is applicable.Comment: 12 pages, 9 figures, accepted for publication in Phys. Rev.

The Role of Bilayer Tilt Difference in Equilibrium Membrane Shapes

Lipid bilayer membranes below their main transition have two tilt order parameters, corresponding to the two monolayers. These two tilts may be strongly coupled to membrane shape but only weakly coupled to each other. We discuss some implications of this observation for rippled and saddle phases, bilayer tubules, and bicontinuous phases. Tilt difference introduces a length scale into the elastic theory of tilted fluid membranes. It can drive an instability of the flat phase; it also provides a simple mechanism for the spontaneous breaking of inversion symmetry seen in some recent experiments.Comment: Latex file; .ps available at http://dept.physics.upenn.edu/~nelson/saddle.p

Nonequilibrium stabilization of charge states in double quantum dots

We analyze the decoherence of charge states in double quantum dots due to cotunneling. The system is treated using the Bloch-Redfield generalized master equation for the Schrieffer-Wolff transformed Hamiltonian. We show that the decoherence, characterized through a relaxation $\tau_{r}$ and a dephasing time $\tau_{\phi}$, can be controlled through the external voltage and that the optimum point, where these times are maximum, is not necessarily in equilibrium. We outline the mechanism of this nonequilibrium-induced enhancement of lifetime and coherence. We discuss the relevance of our results for recent charge qubit experiments.Comment: 5 pages, 5 figure

Escape from a metastable well under a time-ramped force

Thermally activated escape of an over-damped particle from a metastable well under the action of a time-ramped force is studied. We express the mean first passage time (MFPT) as the solution to a partial differential equation, which we solve numerically for a model case. We discuss two approximations of the MFPT, one of which works remarkably well over a wide range of loading rates, while the second is easy to calculate and can provide a valuable first estimate.Comment: 9 pages, including 2 figure