Symmetry in Full Counting Statistics, Fluctuation Theorem, and Relations among Nonlinear Transport Coefficients in the Presence of a Magnetic Field

We study full counting statistics of coherent electron transport through multi-terminal interacting quantum-dots under a finite magnetic field. Microscopic reversibility leads to the symmetry of the cumulant generating function, which generalizes the fluctuation theorem in the context of quantum transport. Using this symmetry, we derive the Onsager-Casimir relation in the linear transport regime and universal relations among nonlinear transport coefficients.Comment: 4.1pages, 1 figur

Fluctuation theorem for entropy production during effusion of a relativistic ideal gas

The probability distribution of the entropy production for the effusion of a relativistic ideal gas is calculated explicitly. This result is then extended to include particle and anti-particle pair production and annihilation. In both cases, the fluctuation theorem is verified.Comment: 6 pages, no figure

A fluctuation theorem for currents and non-linear response coefficients

We use a recently proved fluctuation theorem for the currents to develop the response theory of nonequilibrium phenomena. In this framework, expressions for the response coefficients of the currents at arbitrary orders in the thermodynamic forces or affinities are obtained in terms of the fluctuations of the cumulative currents and remarkable relations are obtained which are the consequences of microreversibility beyond Onsager reciprocity relations

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

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

Thermodynamic time asymmetry in nonequilibrium fluctuations

We here present the complete analysis of experiments on driven Brownian motion and electric noise in a $RC$ circuit, showing that thermodynamic entropy production can be related to the breaking of time-reversal symmetry in the statistical description of these nonequilibrium systems. The symmetry breaking can be expressed in terms of dynamical entropies per unit time, one for the forward process and the other for the time-reversed process. These entropies per unit time characterize dynamical randomness, i.e., temporal disorder, in time series of the nonequilibrium fluctuations. Their difference gives the well-known thermodynamic entropy production, which thus finds its origin in the time asymmetry of dynamical randomness, alias temporal disorder, in systems driven out of equilibrium.Comment: to be published in : Journal of Statistical Mechanics: theory and experimen

Green-Kubo formula for heat conduction in open systems

We obtain an exact Green-Kubo type linear response result for the heat current in an open system. The result is derived for classical Hamiltonian systems coupled to heat baths. Both lattice models and fluid systems are studied and several commonly used implementations of heat baths, stochastic as well as deterministic, are considered. The results are valid in arbitrary dimensions and for any system sizes. Our results are useful for obtaining the linear response transport properties of mesoscopic systems. Also we point out that for systems with anomalous heat transport, as is the case in low-dimensional systems, the use of the standard Green-Kubo formula is problematic and the open system formula should be used.Comment: 4 page

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

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

Gallavotti-Cohen-Type symmetry related to cycle decompositions for Markov chains and biochemical applications

We slightly extend the fluctuation theorem obtained in \cite{LS} for sums of generators, considering continuous-time Markov chains on a finite state space whose underlying graph has multiple edges and no loop. This extended frame is suited when analyzing chemical systems. As simple corollary we derive in a different method the fluctuation theorem of D. Andrieux and P. Gaspard for the fluxes along the chords associated to a fundamental set of oriented cycles \cite{AG2}. We associate to each random trajectory an oriented cycle on the graph and we decompose it in terms of a basis of oriented cycles. We prove a fluctuation theorem for the coefficients in this decomposition. The resulting fluctuation theorem involves the cycle affinities, which in many real systems correspond to the macroscopic forces. In addition, the above decomposition is useful when analyzing the large deviations of additive functionals of the Markov chain. As example of application, in a very general context we derive a fluctuation relation for the mechanical and chemical currents of a molecular motor moving along a periodic filament.Comment: 23 pages, 5 figures. Correction