39,214 research outputs found
Information Geometry, Fluctuations, Non-Equilibrium Thermodynamics, and Geodesics in Complex Systems
Information theory provides an interdisciplinary method to understand important phenomena in many research fields ranging from astrophysical and laboratory fluids/plasmas to biological systems. In particular, information geometric theory enables us to envision the evolution of non-equilibrium processes in terms of a (dimensionless) distance by quantifying how information unfolds over time as a probability density function (PDF) evolves in time. Here, we discuss some recent developments in information geometric theory focusing on time-dependent dynamic aspects of non-equilibrium processes (e.g., time-varying mean value, time-varying variance, or temperature, etc.) and their thermodynamic and physical/biological implications. We compare different distances between two given PDFs and highlight the importance of a path-dependent distance for a time-dependent PDF. We then discuss the role of the information rate Γ=dLdt and relative entropy in non-equilibrium thermodynamic relations (entropy production rate, heat flux, dissipated work, non-equilibrium free energy, etc.), and various inequalities among them. Here, L is the information length representing the total number of statistically distinguishable states a PDF evolves through over time. We explore the implications of a geodesic solution in information geometry for self-organization and control
Measuring the Complexity of Continuous Distributions
We extend previously proposed measures of complexity, emergence, and
self-organization to continuous distributions using differential entropy. This
allows us to calculate the complexity of phenomena for which distributions are
known. We find that a broad range of common parameters found in Gaussian and
scale-free distributions present high complexity values. We also explore the
relationship between our measure of complexity and information adaptation.Comment: 21 pages, 5 Tables, 4 Figure
Fairness Is an Emergent Self-Organized Property of the Free Market for Labor
The excessive compensation packages of CEOs of U.S. corporations in recent
years have brought to the foreground the issue of fairness in economics. The
conventional wisdom is that the free market for labor, which determines the pay
packages, cares only about efficiency and not fairness. We present an
alternative theory that shows that an ideal free market environment also
promotes fairness, as an emergent property resulting from the self-organizing
market dynamics. Even though an individual employee may care only about his or
her salary and no one else's, the collective actions of all the employees,
combined with the profit maximizing actions of all the companies, in a free
market environment under budgetary constraints, lead towards a more fair
allocation of wages, guided by Adam Smith's invisible hand of
self-organization. By exploring deep connections with statistical
thermodynamics, we show that entropy is the appropriate measure of fairness in
a free market environment which is maximized at equilibrium to yield the
lognormal distribution of salaries as the fairest inequality of pay in an
organization under ideal conditions
The Self-Organization of Meaning and the Reflexive Communication of Information
Following a suggestion of Warren Weaver, we extend the Shannon model of
communication piecemeal into a complex systems model in which communication is
differentiated both vertically and horizontally. This model enables us to
bridge the divide between Niklas Luhmann's theory of the self-organization of
meaning in communications and empirical research using information theory.
First, we distinguish between communication relations and correlations among
patterns of relations. The correlations span a vector space in which relations
are positioned and can be provided with meaning. Second, positions provide
reflexive perspectives. Whereas the different meanings are integrated locally,
each instantiation opens global perspectives--"horizons of meaning"--along
eigenvectors of the communication matrix. These next-order codifications of
meaning can be expected to generate redundancies when interacting in
instantiations. Increases in redundancy indicate new options and can be
measured as local reduction of prevailing uncertainty (in bits). The systemic
generation of new options can be considered as a hallmark of the
knowledge-based economy.Comment: accepted for publication in Social Science Information, March 21,
201
Statistical Mechanics and Information-Theoretic Perspectives on Complexity in the Earth System
Peer reviewedPublisher PD
- …