Lattice models for granular-like velocity fields: finite-size effects

in Journal of Statistical Mechanics: Theory and Experiment (2016)

Long-range spatial correlations in the velocity and energy fields of a granular fluid are discussed in the framework of a 1d lattice model. The dynamics of the velocity field occurs through nearest ... [more ▼]

Long-range spatial correlations in the velocity and energy fields of a granular fluid are discussed in the framework of a 1d lattice model. The dynamics of the velocity field occurs through nearest-neighbour inelastic collisions that conserve momentum but dissipate energy. A set of equations for the fluctuating hydrodynamics of the velocity and energy mesoscopic fields give a first approximation for (i) the velocity structure factor and (ii) the finite-size correction to the Haff law, both in the homogeneous cooling regime. At a more refined level, we have derived the equations for the two-site velocity correlations and the total energy fluctuations. First, we seek a perturbative solution thereof, in powers of the inverse of system size. On the one hand, when scaled with the granular temperature, the velocity correlations tend to a stationary value in the long time limit. On the other hand, the scaled standard deviation of the total energy diverges, that is, the system shows multiscaling. Second, we find an exact solution for the velocity correlations in terms of the spectrum of eigenvalues of a certain matrix. The results of numerical simulations of the microscopic model confirm our theoretical results, including the above described multiscaling phenomenon. [less ▲]

Mutual entropy production in bipartite systems

in Journal of Statistical Mechanics: Theory and Experiment (2014)

It was recently shown by Barato et al (2013 Phys. Rev. E 87 042104) that the mutual information at the trajectory level of a bipartite Markovian system is not bounded by the entropy production. In the ... [more ▼]

It was recently shown by Barato et al (2013 Phys. Rev. E 87 042104) that the mutual information at the trajectory level of a bipartite Markovian system is not bounded by the entropy production. In the same way as Gaspard showed (2004 J. Stat. Phys. 117 599) that the entropy production is not directly related to the Shannon entropy at the trajectory level but is in fact equal to its difference from the so-called time-reversed Shannon entropy, we show in this paper that the difference between the mutual information and its time-reversed form is equal to the mutual entropy production (MEP), i.e. the difference between the full entropy production and that of the two marginal processes. Evaluation of the MEP is in general a difficult task due to non-Markovian effects. For bipartite systems, we provide closed expressions in various limiting regimes which we verify by numerical simulations. [less ▲]

Financial interaction networks inferred from traded volumes

in Journal of Statistical Mechanics: Theory and Experiment (2014)

In order to use the advanced inference techniques available for Ising models, we transform complex data (real vectors) into binary strings, using local averaging and thresholding. This transformation ... [more ▼]

In order to use the advanced inference techniques available for Ising models, we transform complex data (real vectors) into binary strings, using local averaging and thresholding. This transformation introduces parameters, which must be varied to characterize the behaviour of the system. The approach is illustrated on financial data, using three inference methods-equilibrium, synchronous and asynchronous inference-to construct functional connections between stocks. We show that the traded volume information is enough to obtain well-known results about financial markets that use, however, presumably richer price information: collective behaviour ('market mode') and strong interactions within industry sectors. Synchronous and asynchronous Ising inference methods give results that are coherent with equilibrium ones and are more detailed since the obtained interaction networks are directed. [less ▲]

Entropy production in quantum Brownian motion

in Journal of Statistical Mechanics: Theory and Experiment (2013), P04005

We investigate how to coherently define entropy production for a process of transient relaxation in the quantum Brownian motion model for the harmonic potential. We compare a form, referred to as ‘poised’ ... [more ▼]

We investigate how to coherently define entropy production for a process of transient relaxation in the quantum Brownian motion model for the harmonic potential. We compare a form, referred to as ‘poised’ (P), which after non-Markovian transients corresponds to a definition of heat as the change in the system Hamiltonian of mean force, with a recent proposal by Esposito et al (ELB) based on a definition of heat as the energy change in the bath. Both expressions yield a positive-definite entropy production and they coincide for vanishing coupling strength, but their difference is proved to be always positive (after non-Markovian transients disappear) and to grow as the coupling strength increases. In the classical ver-damped limit the ‘poised’ entropy production converges to the entropy production used in stochastic thermodynamics. We also investigate the effects of the system size, and of the ensuing Poincar´e recurrences, and how the classical limit is approached. We close by discussing the strongcoupling limit, in which the ideal canonical equilibrium of the bath is violated. [less ▲]

Modified fluctuation-dissipation theorem for general non-stationary states and application to the Glauber-Ising chain

in Journal of Statistical Mechanics: Theory and Experiment (2011), (10), 10025

In this paper, we present a general derivation of a modified fluctuation-dissipation theorem (MFDT) valid near an arbitrary non-stationary state for a system obeying Markovian dynamics. We show that the ... [more ▼]

In this paper, we present a general derivation of a modified fluctuation-dissipation theorem (MFDT) valid near an arbitrary non-stationary state for a system obeying Markovian dynamics. We show that the method for deriving modified fluctuation-dissipation theorems near non-equilibrium stationary states used by Prost et al (2009 Phys. Rev. Lett. 103 090601) is generalizable to non-stationary states. This result follows from both standard linear response theory and from a transient fluctuation theorem, analogous to the Hatano?Sasa relation. We show that this modified fluctuation-dissipation theorem can be interpreted at the trajectory level using the notion of stochastic trajectory entropy in a way which is similar to what has been done recently in the case of the MFDT near non-equilibrium steady states (NESS). We illustrate this framework with two solvable examples: the first example corresponds to a Brownian particle in a harmonic trap subjected to a quench of temperature and to a time-dependent stiffness; the second example is a classic model of coarsening systems, namely the 1D Ising model with Glauber dynamics. [less ▲]

Extracting chemical energy by growing disorder: efficiency at maximum power

in Journal of Statistical Mechanics: Theory and Experiment (2010)

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 ... [more ▼]

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. [less ▲]