arXiv subjects
Publications and source records attributed to Katja Lindenberg.
We derive upper and lower bounds for the efficiency of an isothermal molecular machine operating at maximum power. The upper bound is reached when the activated state is close to the fueling or reactant state (Eyring-like), while the lower bound is reached when the activated state is close to the product state (Kramers-like).
We study the non-equilibrium thermodynamics of a single particle with two available energy levels, in contact with a classical (Maxwell-Boltzmann) or quantum (Bose-Einstein) heat bath. The particle can undergo transitions between the levels via thermal activation or deactivation. The energy levels are alternately raised at a given rate regardless of occupation by the particle, maintaining a fixed energy gap equal to epsilon between them. We explicitly calculate the work, heat and entropy production rates. The efficiency in both the classical and the quantum case goes to a limit between 100% and 50% that depends on the relative rates of particle transitions and level elevation. In the classical problem we explicitly find the large deviation functions for heat, work, and internal energy.
Particles driven through a periodic potential by an external constant force are known to exhibit a pronounced peak of the diffusion around a critical force that defines the transition between locked and running states. It has recently been shown both experimentally and numerically that this peak is greatly enhanced if some amount of spatial disorder is superimposed on the periodic potential. Here we show that beyond a simple enhancement lies a much more interesting phenomenology. For some parameter regimes the system exhibits a rich variety of behaviors from normal diffusion to superdiffusion, subdiffusion and even subtransport.
We study the efficiency at maximum power, $η^*$, of engines performing finite-time Carnot cycles between a hot and a cold reservoir at temperatures $T_h$ and $T_c$, respectively. For engines reaching Carnot efficiency $η_C=1-T_c/T_h$ in the reversible limit (long cycle time, zero dissipation), we find in the limit of low dissipation that $η^*$ is bounded from above by $η_C/(2-η_C)$ and from below by $η_C/2$. These bounds are reached when the ratio of the dissipation during the cold and hot isothermal phases tend respectively to zero or infinity. For symmetric dissipation (ratio one) the Curzon-Ahlborn efficiency $η_{CA}=1-\sqrt{T_c/T_h}$ is recovered.
We implement a binary collision approximation to study pulse propagation in a chain of o-rings. In particular, we arrive at analytic results from which the pulse velocity is obtained by simple quadrature. The predicted pulse velocity is compared to the velocity obtained from the far more resource-intensive numerical integration of the equations of motion. We study chains without precompression, chains precompressed by a constant force at the chain ends (constant precompression), and chains precompressed by gravity (variable precompression). The application of the binary collision approximation to precompressed chains provides an important generalization of a successful theory that had up to this point only been implemented to chains without precompression, that is, to chains in a sonic vacuum.
We present a random walk model that exhibits asymptotic subdiffusive, diffusive, and superdiffusive behavior in different parameter regimes. This appears to be the first instance of a single random walk model leading to all three forms of behavior by simply changing parameter values. Furthermore, the model offers the great advantage of analytic tractability. Our model is non-Markovian in that the next jump of the walker is (probabilistically) determined by the history of past jumps. It also has elements of intermittency in that one possibility at each step is that the walker does not move at all. This rich encompassing scenario arising from a single model provides useful insights into the source of different types of asymptotic behavior.
We study pulse propagation in one-dimensional chains of spherical granules decorated with small randomly-sized granules placed between bigger monodisperse ones. Such "designer chains" are of interest in efforts to control the behavior of the pulse so as to optimize its propagation or attenuation, depending on the desired application. We show that a recently proposed effective description of simple decorated chains can be extended to predict pulse properties in chains decorated with small granules of randomly chosen radii. Furthermore, we also show that the binary collision approximation can again be used to provide analytic results for this system.
Current statistics can be calculated in various ways. Event-based approaches use the statistics of the number of events occuring during a given time. Time-based approaches use the statistics of the time needed to reach a given number of events. By analyzing normal as well as anomalous statistics of nonequilibrium currents through a two level system in contact with two different reservoirs, we investigate the conditions under which these different statistics do or do not yield identical predictions. We rely on the continuous time random walk formulation introduced in our earlier work [Phys. Rev. E 77, 051119 (2008)].
We evaluate the efficiency at maximum power of a quantum-dot Carnot heat engine. The universal value of the coefficients at the linear and quadratic order in the temperature gradient are reproduced. Curzon-Ahlborn efficiency is recovered in the limit of weak dissipation.
Starting from a continuous time random walk (CTRW) model of particles that may evanesce as they walk, our goal is to arrive at macroscopic integro-differential equations for the probability density for a particle to be found at point r at time t given that it started its walk from r_0 at time t=0. The passage from the CTRW to an integro-differential equation is well understood when the particles are not evanescent. Depending on the distribution of stepping times and distances, one arrives at standard macroscopic equations that may be "normal" (diffusion) or "anomalous" (subdiffusion and/or superdiffusion). The macroscopic description becomes considerably more complicated and not particularly intuitive if the particles can die during their walk. While such equations have been derived for specific cases, e.g., for location-independent exponential evanescence, we present a more general derivation valid under less stringent constraints than those found in the current literature.
We investigate the finite time thermodynamics of a single-level fermion system interacting with a thermal reservoir through a tunneling junction. The optimal protocol to extract the maximum work from the system when moving the single energy level between an initial higher value and a final lower value in a finite time is calculated from a quantum master equation. The calculation also yields the optimal protocol to raise the energy level with the expenditure of the least amount of work on the system. The optimal protocol displays discontinuous jumps at the initial and final times.
We study pulse propagation in one-dimensional chains of spherical granules decorated with small grains placed between large granules. The effect of the small granules can be captured by replacing the decorated chains by undecorated chains of large granules of appropriately renormalized mass and effective interaction between the large granules. This allows us to obtain simple analytic expressions for the pulse propagation properties using a generalization of the binary collision approximation introduced in our earlier work [Phys. Rev. E in print (2009); Phys. Rev. E {\bf 69}, 037601 (2004)]
We study the kinetics for the search of an immobile target by randomly moving searchers that detect it only upon encounter. The searchers perform intermittent random walks on a one-dimensional lattice. Each searcher can step on a nearest neighbor site with probability "alpha", or go off lattice with probability "1 - α" to move in a random direction until it lands back on the lattice at a fixed distance L away from the departure point. Considering "alpha" and L as optimization parameters, we seek to enhance the chances of successful detection by minimizing the probability P_N that the target remains undetected up to the maximal search time N. We show that even in this simple model a number of very efficient search strategies can lead to a decrease of P_N by orders of magnitude upon appropriate choices of "alpha" and L. We demonstrate that, in general, such optimal intermittent strategies are much more efficient than Brownian searches and are as efficient as search algorithms based on random walks with heavy-tailed Cauchy jump-length distributions. In addition, such intermittent strategies appear to be more advantageous than Levy-based ones in that they lead to more thorough exploration of visited regions in space and thus lend themselves to parallelization of the search processes.
We derive an exact (classical and quantum) expression for the entropy production of a finite system placed in contact with one or several finite reservoirs each of which is initially described by a canonical equilibrium distribution. Whereas the total entropy of system plus reservoirs is conserved, we show that the system entropy production is always positive and is a direct measure of the system-reservoir correlations and/or entanglements. Using an exactly solvable quantum model, we illustrate our novel interpretation of the Second Law in a microscopically reversible finite-size setting, with strong coupling between system and reservoirs. With this model, we also explicitly show the approach of our exact formulation to the standard description of irreversibility in the limit of a large reservoir.
We consider the efficiency of chemical energy extraction from the environment by the growth of a copolymer made of two constituent units in the entropy-driven regime. We show that the thermodynamic nonlinearity associated with the information processing aspect is responsible for a branching of the system properties such as power, speed of growth, entropy production, and efficiency, with varying affinity. The standard linear thermodynamics argument which predicts an efficiency of 1/2 at maximum power is inappropriate because the regime of maximum power is located either outside of the linear regime or on a separate bifurcated branch, and because the usual thermodynamic force is not the natural variable for this optimization.
We present a theory for the coagulation reaction A+A -> A for particles moving subdiffusively in one dimension. Our theory is tested against numerical simulations of the concentration of $A$ particles as a function of time (``anomalous kinetics'') and of the interparticle distribution function as a function of interparticle distance and time. We find that the theory captures the correct behavior asymptotically and also at early times, and that it does so whether the particles are nearly diffusive or very subdiffusive. We find that, as in the normal diffusion problem, an interparticle gap responsible for the anomalous kinetics develops and grows with time. This corrects an earlier claim to the contrary on our part.
We study pulse propagation in one-dimensional tapered chains of spherical granules. Analytic results for the pulse velocity and other pulse features are obtained using a binary collision approximation. Comparisons with numerical results show that the binary collision approximation provides quantitatively accurate analytic results for these chains.
We present a mean field model for coagulation ($A+A\to A$) and annihilation ($A+A\to 0$) reactions on lattices of traps with a distribution of depths reflected in a distribution of mean escape times. The escape time from each trap is exponentially distributed about the mean for that trap, and the distribution of mean escape times is a power law. Even in the absence of reactions, the distribution of particles over sites changes with time as particles are caught in ever deeper traps, that is, the distribution exhibits aging. Our main goal is to explore whether the reactions lead to further (time dependent) changes in this distribution.