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

Fluctuation theorems for stochastic dynamics

Fluctuation theorems make use of time reversal to make predictions about entropy production in many-body systems far from thermal equilibrium. Here we review the wide variety of distinct, but interconnected, relations that have been derived and investigated theoretically and experimentally. Significantly, we demonstrate, in the context of Markovian stochastic dynamics, how these different fluctuation theorems arise from a simple fundamental time-reversal symmetry of a certain class of observables. Appealing to the notion of Gibbs entropy allows for a microscopic definition of entropy production in terms of these observables. We work with the master equation approach, which leads to a mathematically straightforward proof and provides direct insight into the probabilistic meaning of the quantities involved. Finally, we point to some experiments that elucidate the practical significance of fluctuation relations.Comment: 48 pages, 2 figures. v2: minor changes for consistency with published versio

Entropy production for mechanically or chemically driven biomolecules

Entropy production along a single stochastic trajectory of a biomolecule is discussed for two different sources of non-equilibrium. For a molecule manipulated mechanically by an AFM or an optical tweezer, entropy production (or annihilation) occurs in the molecular conformation proper or in the surrounding medium. Within a Langevin dynamics, a unique identification of these two contributions is possible. The total entropy change obeys an integral fluctuation theorem and a class of further exact relations, which we prove for arbitrarily coupled slow degrees of freedom including hydrodynamic interactions. These theoretical results can therefore also be applied to driven colloidal systems. For transitions between different internal conformations of a biomolecule involving unbalanced chemical reactions, we provide a thermodynamically consistent formulation and identify again the two sources of entropy production, which obey similar exact relations. We clarify the particular role degenerate states have in such a description

Prevalence of dental caries in preschool children by ICDAS diagnostic methodology

Objective: To evaluate the prevalence of caries with the ICDAS index (International Caries Detection and Assessment System) using different cut-off points in children from public and private institutions as well as to associate the presence of caries with socioeconomic indicators, sex, age, type of school (urban or rural) and also family health program with dentist's presence at the school. Material and Methods: An analytical cross-sectional study with a stratified sample (n = 612) in children ranging from three to six years old, in public and private institutions of the city of Barras, State of Piaui, Brazil. The clinical examination was based on ICDAS criteria, and a questionnaire for socioeconomic and educational level data was also applied. Different cut-off points were used, as follows: cut-off point 1 (scores 0 and 1 considered as healthy and scores 2-6 classified as decayed); cut-off point 2 (scores from 0 to 2 classified as healthy, scores 3 to 6 as decayed) and cut-off point 3 (0 to 3 healthy, 4 to 6 decayed). Univariate and Multiple Poisson regression analysis were performed, with 5% significance level. Results: For cut-off point 1, the prevalence was 68.8%; Cut-off point 2, 67.9% and at the cut-off point 3, 60.6%. An association was found in the prevalence of caries with the child's age (p = 0.004), school zone (urban or rural) (p = 0.004) and the presence of the dentist at school (p = 0.001). Conclusion: Taking into account the various cut-off points, the prevalence of caries in preschool children was considered high. The presence of caries lesions is more likely to occur in five year- old boys living in the countryside

Onsager-Machlup theory for nonequilibrium steady states and fluctuation theorems

A generalization of the Onsager-Machlup theory from equilibrium to nonequilibrium steady states and its connection with recent fluctuation theorems are discussed for a dragged particle restricted by a harmonic potential in a heat reservoir. Using a functional integral approach, the probability functional for a path is expressed in terms of a Lagrangian function from which an entropy production rate and dissipation functions are introduced, and nonequilibrium thermodynamic relations like the energy conservation law and the second law of thermodynamics are derived. Using this Lagrangian function we establish two nonequilibrium detailed balance relations, which not only lead to a fluctuation theorem for work but also to one related to energy loss by friction. In addition, we carried out the functional integrals for heat explicitly, leading to the extended fluctuation theorem for heat. We also present a simple argument for this extended fluctuation theorem in the long time limit.Comment: 20 pages, 2 figure