Related papers: Steady state fluctuation relation and time-reversi…
This study deals with continuous limits of interacting one-dimensional diffusive systems, arising from stochastic distortions of discrete curves with various kinds of coding representations. These systems are essentially of a…
We extend previous work to describe a class of fluctuation relations (FRs) that emerge as a consequence of symmetries at the level of stochastic trajectories in Markov chains. We prove that given such a symmetry, and for a suitable…
Stability is a fundamental notion in dynamical systems and control theory that, traditionally understood, describes asymptotic behavior of solutions around an equilibrium point. This notion may be characterized abstractly as continuity of a…
By using recent developments for the Langevin dynamics of spatially asymmetric systems, we routinely generalize the Onsager-Machlup fluctuation theory of the second order in time. In this form, it becomes applicable to fluctuating…
A simple class of chaotic systems in a random environment is considered and the fluctuation theorem is extended under the assumption of reversibility.
The fluctuation relations have received considerable attention since their emergence and development in the 1990s. We present a summary of the main results and suggest ways to interpret this material. Starting with a consideration of the…
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…
A novel method for stability and instability study of autonomous dynamical systems using the flow and divergence of the vector field is proposed. A relation between the method of Lyapunov functions and the proposed method is established.…
This paper is about statistical properties of quasistatic dynamical systems. These are a class of non-stationary systems that model situations where the dynamics change very slowly over time due to external influence. We focus on the case…
When the state of a system may remain bounded even if both the input amplitude and energy are unbounded, then the state bounds given by the standard input-to-state stability (ISS) and integral-ISS (iISS) properties may provide no useful…
Exploring the possibility of describing a fluid flow via a time-reversible equation and its relevance for the fluctuations statistics in stationary turbulent (or laminar) incompressible Navier-Stokes flows.
We present stability and recurrence results for a class of stochastic hybrid dynamical systems with oscillating flow maps. These results are developed by introducing averaging tools that parallel those already existing for ordinary…
In this paper we formulate a dynamical fluctuation theory for stationary non equilibrium states (SNS) which covers situations in a nonlinear hydrodynamic regime and is verified explicitly in stochastic models of interacting particles. In…
Abstract: Models for studying systems in stationary states but out of equilibrium have often empirical nature and very often break the fundamental time reversal symmetry. Here a formal interpretation will be discussed of the widespread idea…
Many nonlinear dynamical systems can be written as Lure systems, which are described by a linear time-invariant system interconnected with a diagonal static sector-bounded nonlinearity. Sufficient conditions are derived for the global…
A time-reversal symmetry relation is established for out-of-equilibrium dilute or rarefied gases described by the fluctuating Boltzmann equation. The relation is obtained from the associated coarse-grained master equation ruling the random…
Considering Langevin dynamics we derive the general form of the stochastic differential that satisfies the Gallavotti-Cohen symmetry. This extends the work previously done by Kurchan, and Lebowitz and Spohn on such systems, and we treat…
A fundamental aspect of turbulence theory is related to the identification of realizable phase-space statistical descriptions able to reproduce in some suitable sense the stochastic fluid equations of a turbulent fluid. In particular, a…
Recent remarkable progress in computing power and numerical analysis is enabling us to fill a gap in the dynamical systems approach to turbulence. One of the significant advances in this respect has been the numerical discovery of simple…
We investigate the instability and stability of specific steady-state solutions of the two-dimensional non-homogeneous, incompressible, and viscous Navier-Stokes equations under the influence of a general potential $f$. This potential is…