Related papers: A deductive statistical mechanics approach for gra…
We present a field theory for the statistics of charge and current fluctuations in diffusive systems. The cumulant generating function is given by the saddle-point solution for the action of this field theory. The action depends on two…
The unique fluctuation-dissipation theorem for equilibrium stands in contrast with the wide variety of nonequilibrium linear response formulae. Their most traditional approach is "analytic", which, in the absence of detailed balance,…
We study the existence of densities for distributions of piecewise deterministic Markov processes. We also obtain relationships between invariant densities of the continuous time process and that of the process observed at jump times. In…
We numerically and theoretically study macroscopic properties of dense, sheared granular materials. In this process we first introduce an invariance in Newton's equations, explain how it leads to Bagnold's scaling, and discuss how it…
We present the conceptual and technical background required to describe and understand the correlations and fluctuations of the empirical density and current of steady-state diffusion processes on all time scales -- observables central to…
We present numerical support for the hypothesis that macroscopic observables of dense granular media can be evaluated from averages over typical blocked configurations: we construct the corresponding measure for a class of…
Seismogenic plate boundaries are presumed to behave in a similar manner to a densely packed granular medium, where fault and blocks systems rapidly rearrange the distribution of forces within themselves, as particles do in slowly sheared…
We consider quasistatic fiber bundle models with interactions. Classical load sharing rules are considered, i.e. local, global or decaying as a power-law of distance. All fibers are identically elastic, initially intact, and break at a…
A quantum mechanical generalization of superstatistics is presented here based on the positive operator valued measure transformation property of the system density matrix. This procedure reveals that the origin of the fluctuating factors…
Motivated by the wide range of applicability of the fluctuation and dissipation phenomena in non-equilibrium systems, we provide a universal study scheme for the dissipation of the energy and the corresponding Brownian motion analysis of…
We consider the asymptotic behavior of the fluctuations for the empirical measures of interacting particle systems with singular kernels. We prove that the sequence of fluctuation processes converges in distribution to a generalized…
Proper modeling of complex systems requires innovative mathematical tools. In this sense, we sought to use deformed or fractal derivatives for studying the dynamics of systems, particularly those, such as granular gases, in which the…
The statistical-physical study of granular matter is essential to understand, from a fundamental point of view, the many different phenomena emerging in these classical many-body systems. Under rapid-flow conditions, granular materials…
We introduce a response-theoretic framework that recasts parameter calibration of ergodic stochastic differential equations as a fluctuation-dissipation problem. Our central result is that the full Jacobian of any stationary observable with…
We present a concise derivation of the Boltzmann form for single-particle energy distributions in classical many-body Hamiltonian systems. The derivation relies on two physical facts: coarse-graining-scale invariance of the empirical…
We discuss the stochastic thermodynamics of systems that are described by a time-dependent density field, for example simple liquids and colloidal suspensions. For a time-dependent change of external parameters, we show that the Jarzynski…
I review the standard paradigm for understanding the formation and evolution of cosmic structure, based on the gravitational instability of dark matter, but many variations on this basic theme are viable. Despite the great progress that has…
Diffusion with stochastic transport is investigated here when the random driving process is a very general Gaussian process, including Fractional Brownian motion. The purpose is the comparison with a deterministic PDE, which in certain…
A Gaussian fluctuation formula is proved for linear statistics of complex random matrices in the case that the statistic is rotationally invariant. For a general linear statistic without this symmetry, Coulomb gas theory is used to predict…
We present an experimental investigation of the statistical properties of spherical granular particles on an inclined plane that are excited by an oscillating side-wall. The data is obtained by high-speed imaging and particle tracking…