Related papers: Deriving GENERIC from a generalized fluctuation sy…
Fluctuation dynamos are generic to turbulent astrophysical systems. The only analytical model of the fluctuation dynamo, due to Kazantsev, assumes the velocity to be delta-correlated in time. This assumption breaks down for any realistic…
We establish a unified fluctuation-response relation for Langevin dynamics. By exploiting the common mathematical structures underlying fluctuations and responses of empirical density and current, we derive a unified identity that…
We consider the higher-order gravity theory derived from the quadratic lagrangian $R+\epsilon R^2$ in vacuum as a first-order (ADM-type) system with constraints, and build time developments of solutions of an initial value formulation of…
We address surface gradient flows which allow for energy dissipation by evolving the surface and a scalar quantity on it, simultaneously. A proper choice of the time derivative and the gauge of surface independence guarantees energy…
We formulate a dynamical fluctuation theory for stationary non equilibrium states (SNS) which is tested explicitly in stochastic models of interacting particles. In our theory a crucial role is played by the time reversed dynamics. Within…
Extended nonequilibrium systems can be studied in the framework of field theory or from dynamical systems perspective. Here we report numerical evidence that the sum of a well-defined number of instantaneous Lyapunov exponents for the…
We propose exact results for the full counting statistics, or the scaled cumulant generating function, pertaining to the transfer of arbitrary conserved quantities across an interface in homogeneous integrable models out of equilibrium. We…
A distributional route to Gaussianity, associated with the concept of Conservative Mixing Transformations in ensembles of random vector-valued variables, is proposed. This route is completely different from the additive mechanism…
The incompressible Navier-Stokes equations contain viscous dissipation but no thermal noise. I show, using a topological argument based on Poincar\'e's lemma, that the fluctuation-dissipation relation for the full nonlinear dynamics can be…
The gauge symmetries of a general dynamical system can be systematically obtained following either a Hamiltonean or a Lagrangean approach. In the former case, these symmetries are generated, according to Dirac's conjecture, by the first…
We compute the growth fluctuations in equilibrium of a wide class of deposition models. These models also serve as general frame to several nearest-neighbor particle jump processes, e.g. the simple exclusion or the zero range process, where…
We propose a class of \textit{Euler-Lagrange} equations indexed by a pair of parameters ($\alpha,r$) that generalizes Nesterov's accelerated gradient methods for convex ($\alpha=1$) and strongly convex ($\alpha=0$) functions from a…
In this article we discuss several aspects of the stochastic dynamics of spin models. The paper has two independent parts. Firstly, we explore a few properties of the multi-point correlations and responses of generic systems evolving in…
Assuming a classical statistical system of point particles the fundamental equations of continuum thermomechanics (continuity equation, equation of motion, and energy equation) shall be derived exactly. The macroscopic state functions…
We discuss geometric formulations of hydrodynamic limits in diffusive systems. Specifically, we describe a geometrical construction in the space of density profiles --- the Wasserstein geometry --- which allows the deterministic…
By extending the Kac-Rice approach to manifolds of finite internal dimension, we show that the mean number $\left\langle\mathcal{N}_\mathrm{tot}\right\rangle$ of all possible equilibria (i.e. force-free configurations, a.k.a. equilibrium…
The global in time existence of solutions of a system describing the interaction of gravitationally attracting particles with a general diffusion term and fixed energy is proved. The presented theory covers the case of the model with…
Microscopic heat engines operate in regimes where thermodynamic quantities fluctuate strongly, making stochastic effects an essential aspect of their performance. However, existing geometric formulations of finite-time thermodynamics…
Starting at the mesoscopic level with a general formulation of stochastic thermodynamics in terms of Markov jump processes, we identify the scaling conditions that ensure the emergence of a (typically nonlinear) deterministic dynamics and…
Thermal fluctuations are a fundamental feature of dissipative systems that are essential for understanding physics near the expected critical point of QCD and in small systems. When such fluctuations are modeled naively in relativistic…