Entropy and efficiency of a molecular motor model

In this paper we investigate the use of path-integral formalism and the concepts of entropy and traffic in the context of molecular motors. We show that together with time-reversal symmetry breaking arguments one can find bounds on efficiencies of such motors. To clarify this techinque we use it on one specific model to find both the thermodynamic and the Stokes efficiencies, although the arguments themselves are more general and can be used on a wide class of models. We also show that by considering the molecular motor as a ratchet, one can find additional bounds on the thermodynamic efficiency

Microscopic heat from the energetics of stochastic phenomena

The energetics of the stochastic process has shown the balance of energy on the mesoscopic level. The heat and the energy defined there are, however, generally different from their macroscopic counterpart. We show that this discrepancy can be removed by adding to these quantities the reversible heat associated with the mesoscopic free energy.Comment: 4 pages, 0 figur

Entropy production and Kullback-Leibler divergence between stationary trajectories of discrete systems

The irreversibility of a stationary time series can be quantified using the Kullback-Leibler divergence (KLD) between the probability to observe the series and the probability to observe the time-reversed series. Moreover, this KLD is a tool to estimate entropy production from stationary trajectories since it gives a lower bound to the entropy production of the physical process generating the series. In this paper we introduce analytical and numerical techniques to estimate the KLD between time series generated by several stochastic dynamics with a finite number of states. We examine the accuracy of our estimators for a specific example, a discrete flashing ratchet, and investigate how close is the KLD to the entropy production depending on the number of degrees of freedom of the system that are sampled in the trajectories.Comment: 14 pages, 7 figure

Stationary and Oscillatory Spatial Patterns Induced by Global Periodic Switching

We propose a new mechanism for pattern formation based on the global alternation of two dynamics neither of which exhibits patterns. When driven by either one of the separate dynamics, the system goes to a spatially homogeneous state associated with that dynamics. However, when the two dynamics are globally alternated sufficiently rapidly, the system exhibits stationary spatial patterns. Somewhat slower switching leads to oscillatory patterns. We support our findings by numerical simulations and discuss the results in terms of the symmetries of the system and the ratio of two relevant characteristic times, the switching period and the relaxation time to a homogeneous state in each separate dynamics.Comment: REVTEX preprint: 12 pages including 1 (B&W) + 3 (COLOR) figures (to appear in Physical Review Letters

Transient fluctuation theorem in closed quantum systems

Our point of departure are the unitary dynamics of closed quantum systems as generated from the Schr\"odinger equation. We focus on a class of quantum models that typically exhibit roughly exponential relaxation of some observable within this framework. Furthermore, we focus on pure state evolutions. An entropy in accord with Jaynes principle is defined on the basis of the quantum expectation value of the above observable. It is demonstrated that the resulting deterministic entropy dynamics are in a sense in accord with a transient fluctuation theorem. Moreover, we demonstrate that the dynamics of the expectation value are describable in terms of an Ornstein-Uhlenbeck process. These findings are demonstrated numerically and supported by analytical considerations based on quantum typicality.Comment: 5 pages, 6 figure

Dissipation: The phase-space perspective

We show, through a refinement of the work theorem, that the average dissipation, upon perturbing a Hamiltonian system arbitrarily far out of equilibrium in a transition between two canonical equilibrium states, is exactly given by $= -\Delta F =kT D(\rho\|\widetilde{\rho})= kT$, where $\rho$ and $\widetilde{\rho}$ are the phase space density of the system measured at the same intermediate but otherwise arbitrary point in time, for the forward and backward process. $D(\rho\|\widetilde{\rho})$ is the relative entropy of $\rho$ versus $\widetilde{\rho}$. This result also implies general inequalities, which are significantly more accurate than the second law and include, as a special case, the celebrated Landauer principle on the dissipation involved in irreversible computations.Comment: 4 pages, 3 figures (4 figure files), accepted for PR

Antarctic ozone variability inside the polar vortex estimated from balloon measurements

Thirteen years of ozone soundings at the Antarctic Belgrano II station (78° S, 34.6° W) have been analysed to establish a climatology of stratospheric ozone and temperature over the area. The station is inside the polar vortex during the period of development of chemical ozone depletion. Weekly periodic profiles provide a suitable database for seasonal characterization of the evolution of stratospheric ozone, especially valuable during wintertime, when satellites and ground-based instruments based on solar radiation are not available. The work is focused on ozone loss rate variability (August–October) and its recovery (November–December) at different layers identified according to the severity of ozone loss. The time window selected for the calculations covers the phase of a quasi-linear ozone reduction, around day 220 (mid-August) to day 273 (end of September). Decrease of the total ozone column over Belgrano during spring is highly dependent on the meteorological conditions. Largest depletions (up to 59%) are reached in coldest years, while warm winters exhibit significantly lower ozone loss (20%). It has been found that about 11% of the total O₃ loss, in the layer where maximum depletion occurs, takes place before sunlight has arrived, as a result of transport to Belgrano of air from a somewhat lower latitude, near the edge of the polar vortex, providing evidence of mixing inside the vortex. Spatial homogeneity of the vortex has been examined by comparing Belgrano results with those previously obtained for South Pole station (SPS) for the same altitude range and for 9 yr of overlapping data. Results show more than 25% higher ozone loss rate at SPS than at Belgrano. The behaviour can be explained taking into account (i) the transport to both stations of air from a somewhat lower latitude, near the edge of the polar vortex, where sunlight reappears sooner, resulting in earlier depletion of ozone, and (ii) the accumulated hours of sunlight, which become much greater at the South Pole after the spring equinox. According to the variability of the ozone hole recovery, a clear connection between the timing of the breakup of the vortex and the monthly ozone content was found. Minimum ozone concentration of 57 DU in the 12–24 km layer remained in November, when the vortex is more persistent, while in years when the final stratospheric warming took place "very early", mean integrated ozone rose by up to 160–180 DU

Mid-winter lower stratosphere temperatures in the Antarctic vortex: comparison between observations and ECMWF operational model.

International audienceRadiosonde temperature profiles from Belgrano (78° S) and other Antarctic stations have been compared with European Centre for Medium-Range Weather Forecasts (ECMWF) data during the winter of 2003. Results show a bias in the operational model which is height and temperature dependent, being too cold at layers peaking at 80 and 25?30 hPa, and hence resulting in an overestimation of the predicted potential PSC areas. Here we show the results of the comparison by considering the possibility of a bias in the sondes at extremely low temperatures and discuss the potential implications that this bias might have on the ozone depletion computed by Climate Transport Model based on ECMWF temperature fields

Parametric phase transition in one dimension

We calculate analytically the phase boundary for a nonequilibrium phase transition in a one-dimensional array of coupled, overdamped parametric harmonic oscillators in the limit of strong and weak spatial coupling. Our results show that the transition is reentrant with respect to the spatial coupling in agreement with the prediction of the mean field theory.Comment: to appear in Europhysics letter