Related papers: On the validity of linear response theory in high-…
The long-term average response of observables of chaotic systems to dynamical perturbations can often be predicted using linear response theory, but not all chaotic systems possess a linear response. Macroscopic observables of complex…
Limit theorems for a linear dynamical system with random interactions are established. These theorems enable us to characterize the dynamics of a large complex system in details and assess whether a large complex system is stable or…
The use of linear response theory for forced dissipative stochastic dynamical systems through the fluctuation dissipation theorem is an attractive way to study climate change systematically among other applications. Here, a mathematically…
Using a sensitive statistical test we determine whether or not one can detect the breakdown of linear response given observations of deterministic dynamical systems. A goodness-of-fit statistics is developed for a linear statistical model…
Basing on the theory of Feynman's influence functional and its hierarchical equations of motion, we develop a linear response theory for quantum open systems. Our theory provides an effective way to calculate dynamical observables of a…
Linear response theory asserts that sufficiently small external biases produce currents proportional to the applied force and forms the theoretical foundation of nonequilibrium transport. Here we demonstrate that linear response can break…
Linear response theory has found many applications in statistical physics. One of these is to compute minimal-work protocols that drive nonequilibrium systems between different thermodynamic states, which are useful for designing engineered…
Linear response theory is a fundamental framework studying the macroscopic response of a physical system to an external perturbation. This paper focuses on the rigorous mathematical justification of linear response theory for Langevin…
For the last two decades, high-dimensional data and methods have proliferated throughout the literature. Yet, the classical technique of linear regression has not lost its usefulness in applications. In fact, many high-dimensional…
Linear Response theory aims to predict how added forcing alters the statistical properties of an unforced system. These kinds of questions have been studied predominantly for autonomous dynamical systems, yet many systems in the physical,…
Linear response theory has developed into a formidable set of tools for studying the forced behaviour of a large variety of systems - including out of equilibrium ones. In this paper we provide a new angle on the problem, by studying under…
A fundamental concept in control theory is that of controllability, where any system state can be reached through an appropriate choice of control inputs. Indeed, a large body of classical and modern approaches are designed for controllable…
For a discrete-time linear system, we use data from a single open-loop experiment to design directly a feedback controller enforcing that a given (polyhedral) set of the state is invariant and given (polyhedral) constraints on the control…
The classical theory of linear response applies to statistical mechanics close to equilibrium. Away from equilibrium, one may describe the microscopic time evolution by a general differentiable dynamical system, identify nonequilibrium…
We present two linked theorems on passivity: the passive behavior theorem, parts 1 and 2. Part 1 provides necessary and sufficient conditions for a general linear system, described by a set of high order differential equations, to be…
Infinite-dimensional control systems with outputs are considered in the Hamiltonian formulation with generalized coordinates. An explicit scheme for constructing a dynamic observer for this class of systems is proposed with arbitrary gain…
Consider a smooth one-parameter family t -> f_t of dynamical systems f_t, with |t|<epsilon. Assume that for all t (or for many t close to t=0) the map f_t admits a unique SRB invariant probability measure m_t. We say that linear response}…
We study general linear transport-reaction systems on an arbitrary dimensional hypercube with periodic boundary conditions. Transport-reaction systems are often used to model the finite speed movement and interaction of particles, bacteria…
It is clear that conventional statistical inference protocols need to be revised to deal correctly with the high-dimensional data that are now common. Most recent studies aimed at achieving this revision rely on powerful approximation…
We develop a linear-algebraic framework for dimensional analysis in systems with constraints, particularly when variables are numerous or related by implicit relations so that direct elimination is impractical. By expressing both…