相关论文: Convexity of mutual information along the heat flo…

We study the convexity of mutual information as a function of time along the flow of the Ornstein-Uhlenbeck process. We prove that if the initial distribution is strongly log-concave, then mutual information is eventually convex, i.e.,…

We study the convexity of mutual information as a function of time along the Fokker-Planck flow. The results are generalizations of that along heat flow and Ornstein-Ulenbeck flow, which were established by A. Wibisono and V. Jog. We prove…

We prove an extended convexity for quantum Fisher information of a mixed state with a given convex decomposition. This convexity introduces a bound which has two parts: i. classical part associated to the Fisher information of the…

We prove that the initial-value problem for the fractional heat equation admits a solution provided that the (possibly unbounded) initial datum has a conveniently moderate growth at infinity. Under the same growth condition we also prove…

We show an energy convexity along any harmonic map heat flow with small initial energy and fixed boundary data on the unit 2-disk. In particular, this gives an affirmative answer to a question raised by W. Minicozzi asking whether such…

We derive a general upper bound to mutual information in terms of the Fisher information. The bound may be further used to derive a lower bound for the Bayesian quadratic cost. These two provide alternatives to other inequalities in the…

The mutual information characterizes correlations between spatially separated regions of a system. Yet, in experiments we often measure dynamical correlations, which involve probing operators that are also separated in time. Here, we…

We construct solutions to the heat equation on convex rings showing that quasiconcavity may not be preserved along the flow, even for smooth and subharmonic initial data.

We show via counterexamples that relative entropy between the solution of a Markovian master equation and the steady state is not a convex function of time. We thus let down a curtain on a possible formulation of a principle of…

It is shown that the diffusion equation and its adjoint (time reversed) equation can be derived with only a few assumptions, using an information-theoretic approach based on the principle of minimum Fisher information

Quantum many-body dynamics generically results in increasing entanglement that eventually leads to thermalization of local observables. This makes the exact description of the dynamics complex despite the apparent simplicity of…

We consider the Cauchy problem for the heat diffusion equation in the whole Euclidean space consisting of two media with different constant conductivities. The large time behavior of temperature, the solution of the problem, is studied when…

Because of the kinematic reversibility of the Stokes equation, fluid mixing at the microscale requires an interplay between advection and diffusion. Here we introduce mutual information between particle positions before and after mixing as…

We study the time evolution of the mutual information between the mass distributions in spatially separated but casually connected regions in an expanding universe. The evolution of the mutual information is primarily determined by the…

We construct a smooth, strictly positive, Gaussian-decaying density on $\mathbb{R}^2$ for which Fisher information along the heat flow is not log-convex. This disproves the Cheng--Geng log-convexity conjecture in dimension two and, by…

We derive general upper bounds to pointwise mutual information in terms of stochastic Fisher information and show these bounds average to known results in the literature for bounds to mutual information in terms of Fisher information. These…

This thesis uses a quantity that is defined and justified by information theory -- mutual information -- to examine models of condensed matter systems. More precisely, it studies models which are made up out of ferromagnetically interacting…

We present two extended forms of Fisher information that fit well in the context of nonextensive thermostatistics. We show that there exists an interplay between these generalized Fisher information, the generalized $q$-Gaussian…

All statistical information about the heat can be obtained with the probability distribution of the heat functional. This paper derives analytically the expression for the distribution of the heat, through path integral, for a diffusive…

Information based thermodynamic logic is revisited. It consists of two parts: Part A applies the modern theory of probability in which an arbitrary convex function \phi is employed as an analytic "device" to express information as…