Related papers: Large deviation theory to model systems under an e…
We discuss the relationships between large deviations in stochastic systems, and "effective interactions" that induce particular rare events. We focus on the nature of these effective interactions in physical systems with many interacting…
A diffusive system coupled to unequal boundary reservoirs reaches a non-equilibrium steady state. While the full-counting-statistics of current fluctuations in these states are well understood for generic systems, results for steady-state…
We prove a large deviations principle for the empirical measure of the one dimensional symmetric simple exclusion process in contact with reservoirs. The dynamics of the reservoirs is slowed down with respect to the dynamics of the system,…
We consider separating the problem of designing Hamiltonian quantum feedback control algorithms into a measurement (estimation) strategy and a feedback (control) strategy, and consider optimizing desirable properties of each under the…
Non-deductive reasoning systems are often {\em representation dependent}: representing the same situation in two different ways may cause such a system to return two different answers. Some have viewed this as a significant problem. For…
A unified treatment for the existence of free energy in several random energy models is presented. If the sequence of distributions associated with the particle systems obeys a large deviation principle, then the free energy exists almost…
For overdamped Langevin systems subjected to weak thermal noise and nonconservative forces, we establish a connection between Freidlin-Wentzell large deviations theory and stochastic thermodynamics. First, we derive a series expansion of…
We study Linear Response Theory and Entropic Fluctuations of finite dimensional non-equilibrium repeated interaction systems (RIS). More precisely, in a situation where the temperatures of the probes can take a finite number of different…
In macroscopic systems behavior is usually reproducible and fluctuations, which are deviations from the typically observed mean values, are small. But almost all inverse problems in the physical and biological sciences are ill-posed and…
Time-irreversible stochastic processes are frequently used in natural sciences to explain non-equilibrium phenomena and to design efficient stochastic algorithms. Our main goal in this thesis is to analyse their dynamics by means of large…
Systems driven away from thermal equilibrium constantly deliver entropy to their environment. Determining this entropy production requires detailed information about the system's internal states and dynamics. However, in most practical…
We establish a link between the phenomenon of Taylor dispersion and the theory of empirical distributions. Using this connection, we derive, upon applying the theory of large deviations, an alternative and much more precise description of…
We use a weak Gibbs property and a weak form of specification to derive level-2 large deviations principles for symbolic systems equipped with a large class of reference measures. This has applications to a broad class of symbolic systems,…
This paper presents convergence analysis of a novel data-driven feedback control algorithm designed for generating online controls based on partial noisy observational data. The algorithm comprises a particle filter-enabled state estimation…
High fidelity state preparation represents a fundamental challenge in the application of quantum technology. While the majority of optimal control approaches use feedback to improve the controller, the controller itself often does not…
Boltzmann-Sanov and Cramer-Chernoff's theorems provide large deviation probabilities, entropy, and rate functions for the spatial distribution of systems and the total internal energy of an ensemble respectively. By the method of Lagrange's…
When a system is perturbed by the variation of external parameters, a lag generally develops between the actual state of the system and the equilibrium state corresponding to the current parameter values. We establish a microscopic,…
This paper investigates a novel offline change-point detection problem from an information-theoretic perspective. In contrast to most related works, we assume that the knowledge of the underlying pre- and post-change distributions are not…
We extend the notion of estimation entropy of autonomous dynamical systems proposed by Liberzon and Mitra [1] to nonlinear dynamical systems with uncertain inputs with bounded variation. We call this new notion the {$\epsilon$}-estimation…
Formalising the confrontation of opinions (models) to observations (data) is the task of Inferential Statistics. Information Theory provides us with a basic functional, the relative entropy (or Kullback-Leibler divergence), an asymmetrical…