Kinetics and thermodynamics of first-order Markov chain copolymerization

We report a theoretical study of stochastic processes modeling the growth of first-order Markov copolymers, as well as the reversed reaction of depolymerization. These processes are ruled by kinetic equations describing both the attachment and detachment of monomers. Exact solutions are obtained for these kinetic equations in the steady regimes of multicomponent copolymerization and depolymerization. Thermodynamic equilibrium is identified as the state at which the growth velocity is vanishing on average and where detailed balance is satisfied. Away from equilibrium, the analytical expression of the thermodynamic entropy production is deduced in terms of the Shannon disorder per monomer in the copolymer sequence. The Mayo-Lewis equation is recovered in the fully irreversible growth regime. The theory also applies to Bernoullian chains in the case where the attachment and detachment rates only depend on the reacting monomer

Microscopic reversibility of quantum open systems

The transition probability for time-dependent unitary evolution is invariant under the reversal of protocols just as in the classical Liouvillian dynamics. In this article, we generalize the expression of microscopic reversibility to externally perturbed large quantum open systems. The time-dependent external perturbation acts on the subsystem during a transient duration, and subsequently the perturbation is switched off so that the total system would thermalize. We concern with the transition probability for the subsystem between the initial and final eigenstates of the subsystem. In the course of time evolution, the energy is irreversibly exchanged between the subsystem and reservoir. The time reversed probability is given by the reversal of the protocol and the initial ensemble. Microscopic reversibility equates the time forward and reversed probabilities, and therefore appears as a thermodynamic symmetry for open quantum systems.Comment: numerical demonstration is correcte

Fluctuation theorem for currents in open quantum systems

A quantum-mechanical framework is set up to describe the full counting statistics of particles flowing between reservoirs in an open system under time-dependent driving. A symmetry relation is obtained which is the consequence of microreversibility for the probability of the nonequilibrium work and the transfer of particles and energy between the reservoirs. In some appropriate long-time limit, the symmetry relation leads to a steady-state quantum fluctuation theorem for the currents between the reservoirs. On this basis, relationships are deduced which extend the Onsager-Casimir reciprocity relations to the nonlinear response coefficients.Comment: 19 page

Fonctionnement hydrologique d'un interfluve sédimentaire de la plaine côtière ancienne de Guyane Française

Le fonctionnement hydrologique de la plaine côtière ancienne de Guyane française constitue une des contraintes majeures à sa mise en valeur agricole, du fait de l'existence de périodes d'excès d'eau prolongées.L'objectif de cet article est d'analyser, sur un interfluve caractéristique de la plaine côtière ancienne, la forme et la dynamique de la nappe et ses sources d'alimentation en relation avec la variabilité des propriétés physiques des sols.Sur le plan expérimental, le travail est conduit à partir d'un suivi hydrologique in situ des fluctuations de la nappe observées sur 21 stations et d'une caractérisation de la variabilité spatiale de la conductivité hydraulique des sols par la méthode du trou de tarière à charge variable. Sur le plan de la modélisation, l'identification de la répartition spatiale de la recharge sur l'interfluve est déterminée par une modélisation inverse. Les suivis montrent d'une part la rapidité de réponse de la nappe aux pluies et d'autre part des temps de présence de la nappe en surface variables selon les sols. La modélisation conforte l'hypothèse d'isolement hydraulique de l'interfluve. La dynamique de la nappe est directement reliée aux entrées pluviométriques et dans une moindre mesure aux sols. La variabilité spatiale de la recharge est par ailleurs sous la dépendance de la topographie et de l'hétérogénéité spatiale de la conductivité hydraulique. Enfin, une estimation du ruissellement de surface souligne son importance sur l'interfluve.Les résultats obtenus montrent que l'engorgement des sols de la plaine côtière est sous la dépendance directe des processus hydrologiques observés à l'échelle de chaque interfluve. La prédiction des zones à excès d'eau marqué et des zones où la recharge est homogène peut être envisagée à partir de la connaissance de la topographie et de la distribution des sols. Sur le plan agronomique et pour les sols à forte contrainte hydrique, la mise en place de systèmes de drainage permettant leur mise en valeur agricole est à considérer.The hydrological behaviour of the old coastal plain in French Guyana causes intense soil waterlogging, which is a major constraint to the agricultural development of this area. The old coastal plain presents a succession of similar old offshore bars (Fig. 1). To elucidate the factors affecting groundwater fluctuations in the plain, the hydrological behaviour of one typical bar was studied. This paper presents the results of the survey of the bar and of the identification of groundwater recharge by inverse modelling. It also investigates the relationships between the spatial variability of recharge rates, the topography, and the soil distribution over the bar to provide means for extrapolation to the whole plain.A bar, covering 0.16 km2, was chosen for the present study (Fig. 2). The maximum relief of the bar is 5 m and its general elevation lies between 2 and 7 m above sea level. The bar is drained by two convergent thalwegs. An important lateral and vertical soil differentiation was observed over a depth of approximately 1 m. Four main soil types (FAO/UNESCO classification) were identified at specific positions on the bar: podzols on the top, ferralsols on the upper slope, alluvial gleysols on the thalwegs and planosolic soils on the mid slope and between ferralsols and podzols. Ferralsols exhibit a progressive increase of clay content with increasing depth. The other soil types present sandy horizons with an irregular textural discontinuity (TD) located at a depth of 70 to 100 cm. Underneath the textural discontinuity lies a sandy clay marine alluvium, which is heterogeneous, ferrallitized and hydromorphic, with lenses of sand and clay. An impervious clay layer (NI) occurs at the base of the bar at an average height of 2 m above sea level. The climate is equatorial and has two marked seasons, wet and dry. Rain is mostly confined to the period November-July, but with a maximum from May to July. Mean annual rainfall is 2700 mm.A network of 21 piezometers was set up at the various topographic and pedological situations (Fig. 3). Six sampling sites were also equipped with tensiometers and access tubes for neutron probes. Groundwater monitoring lasted for three years from 1983 to 1986. The variability of soil hydraulic conductivity over the bar was measured by the auger hole method at the intersections of a 50 m square grid and at 25 m away from a few such intersections. A geostatistical analysis was performed and kriged maps of hydraulic conductivity were produced (Figs. 4 and 5). The comparison between the kriged maps and the soil map indicates that ferralsols exhibit higher conductivities than the other soils.Groundwater monitoring showed three main points. First, a fast response of groundwater fluctuations to rainfall was observed on the bar, which suggests that the hydrology of the bar is little influenced by contributions from neighbouring bars or from the Precambrian basement situated upgradient. Second, time length of soil saturation varied markedly over the bar and was related to the soil types (Fig. 7). Lastly, the observed spatial variability of the hydraulic conductivities and the evolution of water table levels indicate the possibility of a variable distribution of recharge over the bar.The deterministic flow model used for this study, WATASI (WAter TAble SImulation, Wolsack, 1982) is based on a Darcy-Dupuit hydraulic schematization. It is an integrated finite element and multilayer groundwater model with square cells of variable size. Here, three layers were considered: one representing the topsoil, from surface to the textural discontinuity, the second representing the sandy clayey alluvium, lying over the impervious layer, and the third representing the thalwegs surrounding the interfluve (Fig. 10). All layers were divided into cells whose length was either 25 m or 50 m. For the purpose of recharge identification, according to the results of the survey, the cells were grouped in six zones of homogeneous slope and soil type, with each zone assumed to exhibit constant recharge. Calibration of the parameters of the model and identification of recharge over the six zones were conducted over three periods, one exhibiting steady state flow and the two others transient flow, by minimizing the difference between the measured and simulated hydraulic heads. The results obtained by the simulation approach are:- No assumption of lateral inflow is necessary to simulate properly the evolution of hydraulic heads (Figs. 11 and 13); thus groundwater recharge only originates from the seepage of rainfall through the soil cover of the bar. - The spatial variability of recharge appears to follow firstly the slope distribution, and secondly the soil distribution: zones of high recharge correspond to zones of limited waterlogging and vice versa (Figs. 12 and 14). - The estimated rates of recharge are small in comparison to rainfall, and soil water budget calculations demonstrate the existence of large runoff rates. It can be concluded that the waterlogging of soils on the old coastal plain is mainly caused by the hydrological processes at the scale of each bar. Thus, for improving the agricultural suitability of the soils on the plain, local drainage of the waterlogged soils should be sufficient. To predict over the plain which zones should be drained, information on topography and soil distribution can be used as there are good correlations between the variability of these parameters and the variability in groundwater recharge and water table depths

Magnon-driven quantum-dot heat engine

We investigate a heat- to charge-current converter consisting of a single-level quantum dot coupled to two ferromagnetic metals and one ferromagnetic insulator held at different temperatures. We demonstrate that this nano engine can act as an optimal heat to spin-polarized charge current converter in an antiparallel geometry, while it acts as a heat to pure spin current converter in the parallel case. We discuss the maximal output power of the device and its efficiency.Comment: 6 pages, 4 figures, published version, selected as Editor's choic

Single electron transistor strongly coupled to vibrations: Counting Statistics and Fluctuation Theorem

Using a simple quantum master equation approach, we calculate the Full Counting Statistics of a single electron transistor strongly coupled to vibrations. The Full Counting Statistics contains both the statistics of integrated particle and energy currents associated to the transferred electrons and phonons. A universal as well as an effective fluctuation theorem are derived for the general case where the various reservoir temperatures and chemical potentials are different. The first relates to the entropy production generated in the junction while the second reveals internal information of the system. The model recovers Franck-Condon blockade and potential applications to non-invasive molecular spectroscopy are discussed.Comment: extended discussion, to appear in NJ

Fluctuation theorem for the effusion of an ideal gas

The probability distribution of the entropy production for the effusion of an ideal gas between two compartments is calculated explicitly. The fluctuation theorem is verified. The analytic results are in good agreement with numerical data from hard disk molecular dynamics simulations.Comment: 11 pages, 10 figures, 2 table

Les structures synsédimentaires miocènes en compression associées au décrochement dextre Mhrila-Chérichira (Tunisie centrale)

L'étude de l'accident tectonique Mhrila-Chérichira (Tunisie centrale) met en évidence la permanence de son activité depuis le Crétacé inférieur jusqu'au Villafranchien et permet de retracer l'évolution tectonique de cette région

Modified Fluctuation-dissipation theorem for non-equilibrium steady-states and applications to molecular motors

We present a theoretical framework to understand a modified fluctuation-dissipation theorem valid for systems close to non-equilibrium steady-states and obeying markovian dynamics. We discuss the interpretation of this result in terms of trajectory entropy excess. The framework is illustrated on a simple pedagogical example of a molecular motor. We also derive in this context generalized Green-Kubo relations similar to the ones derived recently by Seifert., Phys. Rev. Lett., 104, 138101 (2010) for more general networks of biomolecular states.Comment: 6 pages, 2 figures, submitted in EP

General properties of response functions of nonequilibrium steady states

We derive general properties, which hold for both quantum and classical systems, of response functions of nonequilibrium steady states. We clarify differences from those of equilibrium states. In particular, sum rules and asymptotic behaviors are derived, and their implications are discussed. Since almost no assumptions are made, our results are applicable to diverse physical systems. We also demonstrate our results by a molecular dynamics simulation of a many-body interacting system.Comment: After publication of this paper, several typos were found, which have been fixed in the erratum (J. Phys. Soc. Jpn., 80 (2011) 128001). All the corrections have been made in this updated arXive version. 13 pages with 3 figure