Related papers: A maximum entropy framework for non-exponential di…
Boltzmann-Gibbs distribution arises as the statistical equilibrium probability distribution of money among the agents of a closed economic system where random and undirected exchanges are allowed. When considering a model with uniform…
In addition to the well known common properties such as small world and community structures, recent empirical investigations suggest a universal scaling law for the spatial structure of social networks. It is found that the probability…
Since its origin in the thermodynamics of the 19th century, the concept of entropy has also permeated other fields of physics and mathematics, such as Classical and Quantum Statistical Mechanics, Information Theory, Probability Theory,…
Maximum entropy models are increasingly being used to describe the collective activity of neural populations with measured mean neural activities and pairwise correlations, but the full space of probability distributions consistent with…
Certain fluctuations in particle number at fixed total energy lead exactly to a cut-power law distribution in the one-particle energy, via the induced fluctuations in the phase-space volume ratio. The temperature parameter is expressed…
We consider the maximum entropy problems associated with R\'enyi $Q$-entropy, subject to two kinds of constraints on expected values. The constraints considered are a constraint on the standard expectation, and a constraint on the…
Most astrophysical plasmas are observed to have velocity distribution functions exhibiting non-Maxwellian suprathermal tails. The high energy particle populations are accurately represented by the family of kappa-distributions where the use…
This paper generalizes the entropy maximization problem leading to the Boltzmann-Gibbs distribution through the nonadditive entropy $S_{q,s}(p)=k_{s}\sum^{W}_{i\geq1}p_{i}\ln_{q}1/p_{i}$, $q\in(0,1)$, which is a rescaled version of $S_{q}$…
A plethora of natural, artificial and social systems exist which do not belong to the Boltzmann-Gibbs (BG) statistical-mechanical world, based on the standard additive entropy $S_{BG}$ and its associated exponential BG factor. Frequent…
Behavior of condensed matter systems deviating from the standard equilibrium conditions is discussed. Statistical properties of coupled dynamic-stochastic systems are studied within a combination of the maximum information principle and the…
Quasi-power law ensembles are discussed from the perspective of nonextensive Tsallis distributions characterized by a nonextensive parameter $q$. A number of possible sources of such distributions are presented in more detail. It is further…
Mounting evidences are being gathered suggesting that income and wealth distribution in various countries or societies follow a robust pattern, close to the Gibbs distribution of energy in an ideal gas in equilibrium, but also deviating…
We generalize the usual exponential Boltzmann factor to any reasonable and potentially observable distribution function, $B(E)$. By defining generalized logarithms $\Lambda$ as inverses of these distribution functions, we are led to a…
This work focuses on off-policy evaluation (OPE) with function approximation in infinite-horizon undiscounted Markov decision processes (MDPs). For MDPs that are ergodic and linear (i.e. where rewards and dynamics are linear in some known…
The thermodynamic maximum principle for the Boltzmann-Gibbs-Shannon (BGS) entropy is reconsidered by combining elements from group and measure theory. Our analysis starts by noting that the BGS entropy is a special case of relative entropy.…
Starting from microcanonical basis with the principle of equal a priori probability, it is found that, besides ordinary Boltzmann-Gibbs theory with the exponential distribution, a theory describing systems with power-law distributions can…
The Boltzmann distribution (the most probable distribution) is one of the most important concepts used in physics, chemistry and biology. Suppose we put the system initially in one of the less probable state then the system will find the…
This paper introduces nonparametric econometric methods that characterize general power law distributions under basic stability conditions. These methods extend the literature on power laws in the social sciences in several directions.…
In this paper, we propose an optimization-based mechanism to explain power law distributions, where the function that the optimization process is seeking to optimize is derived mathematically, then the behavior and interpretation of this…
A fundamental problem in analysis of complex systems is getting a reliable estimate of entropy of their probability distributions over the state space. This is difficult because unsampled states can contribute substantially to the entropy,…