Related papers: de Bruijn-type identity for systems with flux
We show how some attractive information--theoretic properties of Gaussians pass over to more general families of stable densities. We define a new score function for symmetric stable laws, and use it to give a stable version of the heat…
We investigate free-energy dissipation in a continuous-time birth-and-death dynamics in $\mathbb{R}^d$. For these Markov processes, the class of reversible measures coincides with the infinite-volume Gibbs point processes for some…
This paper focuses on proving the equivalence between Stein's identity and de Bruijn's identity. Given some conditions, we prove that Stein's identity is equivalent to de Bruijn's identity. In addition, some extensions of de Bruijn's…
Von Neumann entropy rate for open quantum systems is, in general, written in terms of entropy production and entropy flow rates, encompassing the second law of thermodynamics. When the open-quantum-system evolution corresponds to a quantum…
We establish an exact identity for overdamped Langevin dynamics: the total entropy production rate equals four times the mutual information rate between an infinitesimal displacement and its time midpoint, plus a mean flow term. This yields…
We study conditional mutual information (cMI) between a pair of variables $X,Y$ given a third one $Z$ and derived quantities including transfer entropy (TE) and causation entropy (CE) in the dynamically relevant context where $X=T(Y,Z)$ is…
Motivated by the classical De Bruijn's identity for the additive Gaussian noise channel, in this paper we consider a generalized setting where the channel is modelled via stochastic differential equations driven by fractional Brownian…
We show that the no-deleting and no-cloning principles are implications of information conservation principle. This is unlike in classical physics, where cloning and deleting are possible, independently of information conservation.…
In the dynamics of open quantum systems, the backflow of information to the reduced system under study has been suggested as the actual physical mechanism inducing memory and thus leading to non-Markovian quantum dynamics. To this aim, the…
Binary time series data are very common in many applications, and are typically modelled independently via a Bernoulli process with a single probability of success. However, the probability of a success can be dependent on the outcome…
In this paper we propose the use of concepts from thermodynamics in the study of crowd dynamics. Our continuous model consists of the continuity equation for the density of the crowd and a kinetic equation for the velocity field. The latter…
Binary data are highly common in many applications, however it is usually modelled with the assumption that the data are independently and identically distributed. This is typically not the case in many real-world examples and such the…
A special type of cyclic sequences named adjacency-hopping de Bruijn sequences is introduced in this paper. It is theoretically proved the existence of such sequences, and the number of such sequences is derived. These sequences guarantee…
Kawai, Parrondo, and Van den Broeck [Phys. Rev. Lett. 98, 080602 (2007)] have recently established a quantitative relationship between dissipated work and a microscopic, information-theoretic measure of irreversibility. We illustrate this…
The response of thermodynamic systems perturbed out of an equilibrium steady-state is described by the reciprocal and the fluctuation-dissipation relations. The so-called fluctuation theorems extended the study of fluctuations far beyond…
We study a class of nonlinear nonlocal conservation laws with discontinuous flux, modeling crowd dynamics and traffic flow, without any additional conditions on finiteness/discreteness of the set of discontinuities or on the monotonicity of…
We consider consistent particle systems, which include independent random walkers, the symmetric exclusion and inclusion processes, as well as the dual of the KMP model. Consistent systems are such that the distribution obtained by first…
Applying the theory of self-adjoint extensions of Hermitian operators to Koopman von Neumann classical mechanics, the most general set of probability distributions is found for which entropy is conserved by Hamiltonian evolution. A new…
A general relation between entropy and an evolutionary superoperator is derived based on the theory of the real-time formulation. The formulation establishing the relation relies only on the framework of quantum statistical mechanics and…
The deep connection between entropy and information is discussed in terms of both classical and quantum physics. The mechanism of information transfer between systems via entanglement is explored in the context of decoherence theory. The…