Fisher Information and Complexity Measure of Generalized Morse Potential Model

The spreading of the quantum-mechanical probability distribution density of the three-dimensional system is quantitatively determined by means of the local information-theoretic quantity of the Shannon information and information energy in both position and momentum spaces. The complexity measure which is equivalent to Cramer-Rao uncertainty product is determined. We have obtained the information content stored, the concentration of quantum system and complexity measure numerically for n=0, 1, 2 and 3 respectively.     

Information and complexity measures in the interface of a metal and a superconductor

Fisher information, Shannon information entropy and Statistical Complexity are calculated for the interface of a normal metal and a superconductor, as a function of the temperature for several materials. The order parameter $\mathrm{\Psi }(\mathbf{r})$ derived from the Ginzburg–Landau theory is used as an input together with experimental values of critical transition temperature $T_c$ and the superconducting coherence length ${\xi }_0$. Analytical expressions are obtained for information and complexity measures. Thus $T_c$ is directly related in a simple way with disorder and complexity. An analytical relation is found of the Fisher Information with the energy profile of superconductivity i.e. the ratio of surface free energy and the bulk free energy. We verify that a simple relation holds between Shannon and Fisher information i.e. a decomposition of a global information quantity (Shannon) in terms of two local ones (Fisher information), previously derived and verified for atoms and molecules by Liu et al. Finally, we find analytical expressions for generalized information measures like the Tsallis entropy and Fisher information. We conclude that the proper value of the non-extensivity parameter $q?1$, in agreement with previous work using a different model, where $q?1.005$.     

Information dynamics: temporal behavior of uncertainty measures

We carry out a systematic study of uncertainty measures that are generic to dynamical processes of varied origins, provided they induce suitable continuous probability distributions. The major technical tools are the information theory methods and inequalities satisfied by Fisher and Shannon information measures. We focus on the compatibility of these inequalities with the prescribed (deterministic, random or quantum) temporal behavior of pertinent probability densities.      

Quantum Information and Entropy

Thermodynamic entropy is not an entirely satisfactory measure of information of a quantum state. This entropy for an unknown pure state is zero, although repeated measurements on copies of such a pure state do communicate information. In view of this, we propose a new measure for the informational entropy of a quantum state that includes information in the pure states and the thermodynamic entropy. The origin of information is explained in terms of an interplay between unitary and non-unitary evolution. Such complementarity is also at the basis of the so-called interaction-free measurement.     

Information and Self-Organization II: Steady State and Phase Transition

This paper starts from Schrödinger’s famous question “what is life” and elucidates answers that invoke, in particular, Friston’s free energy principle and its relation to the method of Bayesian inference and to Synergetics 2nd foundation that utilizes Jaynes’ maximum entropy principle. Our presentation reflects the shift from the emphasis on physical principles to principles of information theory and Synergetics. In view of the expected general audience of this issue, we have chosen a somewhat tutorial style that does not require special knowledge on physics but familiarizes the reader with concepts rooted in information theory and Synergetics.     

A Photon Force and Flow for Dissipative Structuring: Application to Pigments,Plants and Ecosystems

Through a modern derivation of Planck’s formula for the entropy of an arbitrary beam of photons, we derive a general expression for entropy production due to the irreversible process of the absorption of an arbitrary incident photon spectrum in material and its dissipation into an infrared-shifted grey-body emitted spectrum, with the rest being reflected or transmitted. Employing the framework of Classical Irreversible Thermodynamic theory, we define the generalized thermodynamic flow as the flow of photons from the incident beam into the material and the generalized thermodynamic force is, then, the entropy production divided by the photon flow, which is the entropy production per unit photon at a given wavelength. We compare the entropy production of different inorganic and organic materials (water, desert, leaves and forests) under sunlight and show that organic materials are the greater entropy-producing materials. Intriguingly, plant and phytoplankton pigments (including chlorophyll) reach peak absorption exactly where entropy production through photon dissipation is maximal for our solar spectrum 430<λ<550 nm, while photosynthetic efficiency is maximal between 600 and 700 nm. These results suggest that the evolution of pigments, plants and ecosystems has been towards optimizing entropy production, rather than photosynthesis. We propose using the wavelength dependence of global entropy production as a biosignature for discovering life on planets of other stars.     

Information,Entropy, Life,and the Universe

In 2015, I wrote a book with the same title as this article. The book’s subtitle is: “What we know and what we do not know.” On the book’s dedication page, I wrote: “This book is dedicated to readers of popular science books who are baffled, perplexed, puzzled, astonished, confused, and discombobulated by reading about Information, Entropy, Life and the Universe.” In the first part of this article, I will present the definitions of two central concepts: the “Shannon measure of information” (SMI), in Information Theory, and “Entropy”, in Thermodynamics. Following these definitions, I will discuss the framework of their applicability. In the second part of the article, I will examine the question of whether living systems and the entire universe are, or are not within the framework of applicability of the concepts of SMI and Entropy. I will show that much of the confusion that exists in the literature arises because of people’s ignorance about the framework of applicability of these concepts.     

Efficient Markets and Contingent Claims Valuation: An Information Theoretic Approach

This research article shows how the pricing of derivative securities can be seen from the context of stochastic optimal control theory and information theory. The financial market is seen as an information processing system, which optimizes an information functional. An optimization problem is constructed, for which the linearized Hamilton–Jacobi–Bellman equation is the Black–Scholes pricing equation for financial derivatives. The model suggests that one can define a reasonable Hamiltonian for the financial market, which results in an optimal transport equation for the market drift. It is shown that in such a framework, which supports Black–Scholes pricing, the market drift obeys a backwards Burgers equation and that the market reaches a thermodynamical equilibrium, which minimizes the free energy and maximizes entropy.     

Volatility Dynamics of Non-Linear Volatile Time Series and Analysis of Information Flow: Evidence from Cryptocurrency Data

This paper aims to empirically examine long memory and bi-directional information flow between estimated volatilities of highly volatile time series datasets of five cryptocurrencies. We propose the employment of Garman and Klass (GK), Parkinson’s, Rogers and Satchell (RS), and Garman and Klass-Yang and Zhang (GK-YZ), and Open-High-Low-Close (OHLC) volatility estimators to estimate cryptocurrencies’ volatilities. The study applies methods such as mutual information, transfer entropy (TE), effective transfer entropy (ETE), and Rényi transfer entropy (RTE) to quantify the information flow between estimated volatilities. Additionally, Hurst exponent computations examine the existence of long memory in log returns and OHLC volatilities based on simple R/S, corrected R/S, empirical, corrected empirical, and theoretical methods. Our results confirm the long-run dependence and non-linear behavior of all cryptocurrency’s log returns and volatilities. In our analysis, TE and ETE estimates are statistically significant for all OHLC estimates. We report the highest information flow from BTC to LTC volatility (RS). Similarly, BNB and XRP share the most prominent information flow between volatilities estimated by GK, Parkinson’s, and GK-YZ. The study presents the practicable addition of OHLC volatility estimators for quantifying the information flow and provides an additional choice to compare with other volatility estimators, such as stochastic volatility models.     

Switching and Swapping of Quantum Information: Entropy and Entanglement Level

Information switching and swapping seem to be fundamental elements of quantum communication protocols. Another crucial issue is the presence of entanglement and its level in inspected quantum systems. In this article, a formal definition of the operation of the swapping local quantum information and its existence proof, together with some elementary properties analysed through the prism of the concept of the entropy, are presented. As an example of the local information swapping usage, we demonstrate a certain realisation of the quantum switch. Entanglement levels, during the work of the switch, are calculated with the Negativity measure and a separability criterion based on the von Neumann entropy, spectral decomposition and Schmidt decomposition. Results of numerical experiments, during which the entanglement levels are estimated for systems under consideration with and without distortions, are presented. The noise is generated by the Dzyaloshinskii-Moriya interaction and the intrinsic decoherence is modelled by the Milburn equation. This work contains a switch realisation in a circuit form—built out of elementary quantum gates, and a scheme of the circuit which estimates levels of entanglement during the switch’s operating.     

Prebiotic Aggregates (Tissues) Emerging from Reaction–Diffusion: Formation Time,Configuration Entropy and Optimal Spatial Dimension

For the formation of a proto-tissue, rather than a protocell, the use of reactant dynamics in a finite spatial region is considered. The framework is established on the basic concepts of replication, diversity, and heredity. Heredity, in the sense of the continuity of information and alike traits, is characterized by the number of equivalent patterns conferring viability against selection processes. In the case of structural parameters and the diffusion coefficient of ribonucleic acid, the formation time ranges between a few years to some decades, depending on the spatial dimension (fractional or not). As long as equivalent patterns exist, the configuration entropy of proto-tissues can be defined and used as a practical tool. Consequently, the maximal diversity and weak fluctuations, for which proto-tissues can develop, occur at the spatial dimension 2.5.     

The Natural Philosophy of Economic Information: Autonomous Agents and Physiosemiosis

Information is a core concept in modern economics, yet its definition and empirical specification is elusive. One reason is the intellectual grip of the Shannon paradigm which marginalizes semantic information. However, a precise concept of economic information must be based on a theory of semantics, since what counts economically is the meaning, function and use of information. This paper introduces a new principled approach to information that adopts the paradigm of biosemiotics, rooted in the philosophy of Charles S. Peirce and builds on recent developments of the thermodynamics of information. Information processing by autonomous agents, defined as autopoietic heat engines, is conceived as physiosemiosis operating according to fundamental thermodynamic principles of information processing, as elucidated in recent work by Kolchinsky and Wolpert (KW). I plug the KW approach into a basic conceptual model of physiosemiosis and present an evolutionary interpretation. This approach has far-reaching implications for economics, such as suggesting an evolutionary view of the economic agent, choice and behavior, which is informed by applications of statistical thermodynamics on the brain.