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Entropic Dynamics is a framework in which dynamical laws are derived as an application of entropic methods of inference. No underlying action principle is postulated. Instead, the dynamics is driven by entropy subject to the constraints…
In recent years, the unified theory of information and thermodynamics has been intensively discussed in the context of stochastic thermodynamics. The unified theory reveals that information theory would be useful to understand…
We define {\em predictive information} $I_{\rm pred} (T)$ as the mutual information between the past and the future of a time series. Three qualitatively different behaviors are found in the limit of large observation times $T$: $I_{\rm…
In this paper we present a discussion of the basic aspects of the well-known problem of prediction and inference in physics, with specific attention to the role of models, the use of data and the application of recent developments in…
General characterization of physical measurements is discussed within the framework of a classical information theory. Uncertainty relation for simultaneous measurements of two physical observables is defined in this framework for…
We theoretically investigate how information flows when two particles interact with each other. Understanding the physical mechanisms of directional information flow is crucial for advancing information thermodynamics and stochastic…
The abundance of different species in a community often follows the log series distribution. Other ecological patterns also have simple forms. Why does the complexity and variability of ecological systems reduce to such simplicity? Common…
A unifying theory is put forward that entropy is equal to action. The crowning derivation is based on information theoretic methods and uses our hypothesis that "particles move via the discrete Bernoulli Process." While this hypothesis…
Financial markets convert the incremental arrival of information into asset price changes. In a sandpile model grains of sand represent bits of data, and the size of an avalanche, governed by a scaling law, is linked to price volatility.…
How can we enable machines to make sense of the world, and become better at learning? To approach this goal, I believe viewing intelligence in terms of many integral aspects, and also a universal two-term tradeoff between task performance…
Information geometry uses the formal tools of differential geometry to describe the space of probability distributions as a Riemannian manifold with an additional dual structure. The formal equivalence of compositional data with discrete…
Complex systems are found in most branches of science. It is still argued how to best quantify their complexity and to what end. One prominent measure of complexity (the statistical complexity) has an operational meaning in terms of the…
Since Bachelier's thesis in 1900 (laying the foundation of the stochastic process, or Brownian motion, as a model of stock price changes), attempts at understanding the nature of prices and at predicting them have failed. Statistical…
It is shown that the standard expression for the information entropy, originally due to Shannon, is only valid for a particular set of states. For the general case of statistical mechanics, one needs to include an additional term in the…
Modelling accurately financial price variations is an essential step underlying portfolio allocation optimization, derivative pricing and hedging, fund management and trading. The observed complex price fluctuations guide and constraint our…
As early indicated by Charles Darwin, languages behave and change very much like living species. They display high diversity, differentiate in space and time, emerge and disappear. A large body of literature has explored the role of…
According to quantum mechanics, the informational content of isolated systems does not change in time. However, subadditivity of entropy seems to describe an excess of information when we look at single parts of a composite systems and…
We show that the global balance of information dynamics for general quantum measurements given in [F. Buscemi, M. Hayashi, and M. Horodecki, Phys.Rev.Lett. 100, 210504 (2008)] makes it possible to unify various and generally inequivalent…
While most useful information theoretic inequalities can be deduced from the basic properties of entropy or mutual information, Shannon's entropy power inequality (EPI) seems to be an exception: available information theoretic proofs of the…
We try to establish a unified information theoretic approach to learning and to explore some of its applications. First, we define {\em predictive information} as the mutual information between the past and the future of a time series,…