Related papers: Random Dynamics, Entropy Production and Fisher Inf…

Shannon information entropy is a natural measure of probability (de)localization and thus (un)predictability in various procedures of data analysis for model systems. We pay particular attention to links between the Shannon entropy and the…

Filtering theory gives an explicit models for the flow of information and thereby quantifies the rates of change of information supplied to and dissipated from the filter's memory. Here we extend the analysis of Mitter and Newton from…

Shannon entropy and Fisher information functionals are known to quantify certain information-theoretic properties of continuous probability distributions of various origins. We carry out a systematic study of these functionals, while…

Transfer Entropy and Directed Information are information-theoretic measures of the directional dependency between stochastic processes. Following the definitions of Schreiber and Massey in discrete time, we define and evaluate these…

We introduce the Fisher information in the basis of decay modes of Markovian dynamics, arguing that it encodes important information about the behavior of nonequilibrium systems. In particular we generalize an orthonormality relation…

Markov Random Field models are powerful tools for the study of complex systems. However, little is known about how the interactions between the elements of such systems are encoded, especially from an information-theoretic perspective. In…

For a network of discrete states with a periodically driven Markovian dynamics, we develop an inference scheme for an external observer who has access to some transitions. Based on waiting-time distributions between these transitions, the…

For a Markovian dynamics on discrete states, the logarithmic ratio of waiting-time distributions between two successive, instantaneous transitions in forward and backward direction is a measure of time-irreversibility. It thus serves as an…

I critically examine the notion of ``irreversibility,'' and discuss in what sense it applies to the spontaneous creation of particles in external fields. The investigation reveals that particle creation in very strong fields can only be…

In the previous papers (Kui\'{c} et al. in Found Phys 42:319-339, 2012; Kui\'{c} in arXiv:1506.02622, 2015), it was demonstrated that applying the principle of maximum information entropy by maximizing the conditional information entropy,…

Using the transport-of-intensity approach for free-space optical propagation in the paraxial regime, we show that diffraction is fundamentally related to the Fisher information associated with models of the transverse intensity…

We explore the dynamics of information systems. We show that the driving force for information dynamics is determined by both the information landscape and information flux which determines the equilibrium time reversible and the…

In this paper we introduce a new generalisation of the relative Fisher Information for Markov jump processes on a finite or countable state space, and prove an inequality which connects this object with the relative entropy and a large…

We establish a variant of the log-Sobolev and transport-information inequalities for mixture distributions. If a probability measure $\pi$ can be decomposed into components that individually satisfy such inequalities, then any measure $\mu$…

Stochastic thermodynamics provides the framework to analyze thermodynamic laws and quantities along individual trajectories of small but fully observable systems. If the observable level fails to capture all relevant degrees of freedom,…

Spiking activity from populations of neurons display causal interactions and memory effects. Therefore, they are expected to show some degree of irreversibility in time. Motivated by the spike train statistics, in this paper we build a…

The dissipation of general convex entropies for continuous time Markov processes can be described in terms of backward martingales with respect to the tail filtration. The relative entropy is the expected value of a backward submartingale.…

We analyze F\"urth's 1933 classical uncertainty relations in the modern language of stochastic differential equations. Our interest is motivated by applications to non-equilibrium classical statistical mechanics. We show that F\"urth's…

We consider a drift-diffusion process of $N$ stochastic particles and show that its empirical measure converges, as $N\rightarrow \infty$, to the solution of the Landau equation. We work in the regime of very soft and Coulomb potentials…

We present a novel synthesis of Fisher information and asset pricing theory that yields a practical method for reconstructing the probability density implicit in security prices. The Fisher information approach to these inverse problems…