Related papers: Incomplete descriptions and relevant entropies
We review with a tutorial scope the information theory foundations of quantum statistical physics. Only a small proportion of the variables that characterize a system at the microscopic scale can be controlled, for both practical and…
Statistical mechanics is generalized on the basis of an information theory for inexact or incomplete probability distributions. A parameterized normalization is proposed and leads to a nonextensive entropy. The resulting incomplete…
When constructing models of the world, we aim for optimal compressions: models that include as few details as possible while remaining as accurate as possible. But which details -- or features measured in data -- should we choose to include…
Maximum Entropy is a powerful concept that entails a sharp separation between relevant and irrelevant variables. It is typically invoked in inference, once an assumption is made on what the relevant variables are, in order to estimate a…
Statistical mechanics is generalized on the basis of an additive information theory for incomplete probability distributions. The incomplete normalization $\sum_{i=1}^wp_i^q=1$ is used to obtain generalized entropy $S=-k\sum_{i=1}^wp_i^q\ln…
Maximum entropy principle identifies forces conjugated to observables and the thermodynamic relations between them, independent upon their underlying mechanistic details. For data about state distributions or transition statistics, the…
The present paper is meant to give a simple introduction to the problem of the connection between microscopic dynamics and statistical laws. For sake of simplicity, we mostly refer to non-dissipative dynamics, since dissipation adds…
By assuming an appropriate energy composition law between two systems governed by the same non-extensive entropy, we revisit the definitions of temperature and pressure, arising from the zeroth principle of thermodynamics, in a manner…
These lectures deal with the problem of inductive inference, that is, the problem of reasoning under conditions of incomplete information. Is there a general method for handling uncertainty? Or, at least, are there rules that could in…
The maximum entropy principle (MEP) apparently allows us to derive, or justify, fundamental results of equilibrium statistical mechanics. Because of this, a school of thought considers the MEP as a powerful and elegant way to make…
Formalising the confrontation of opinions (models) to observations (data) is the task of Inferential Statistics. Information Theory provides us with a basic functional, the relative entropy (or Kullback-Leibler divergence), an asymmetrical…
The principle of maximum entropy is a broadly applicable technique for computing a distribution with the least amount of information possible constrained to match empirical data, for instance, feature expectations. We seek to generalize…
Statistical physics aims to describe properties of macroscale systems in terms of distributions of their microscale agents. Its central tool is the maximization of entropy, a variational principle. We review the history of this principle,…
In statistical mechanics, measuring the number of available states and their probabilities, and thus the system's entropy, enables the prediction of the macroscopic properties of a physical system at equilibrium. This predictive capacity…
Predictive statistical mechanics is a form of inference from available data, without additional assumptions, for predicting reproducible phenomena. By applying it to systems with Hamiltonian dynamics, a problem of predicting the macroscopic…
A definition of the thermodynamic entropy based on the time-dependent probability distribution of the macroscopic variables is developed. When a constraint in a composite system is released, the probability distribution for the new…
A new axiomatic characterization with a minimum of conditions for entropy as a function on the set of states in quantum mechanics is presented. Traditionally unspoken assumptions are unveiled and replaced by proven consequences of the…
I give a concise introduction to some essential concepts of statistical mechanics: 1. Probability theory (constrained distributions, concentration theorem, frequency estimation, hypothesis testing); 2. Macroscopic systems in equilibrium…
In this document, we aim to gather various results related to a compositional/categorical approach to rigorous Statistical Mechanics. Rigorous Statistical Mechanics is centered on the mathematical study of statistical systems. Central…
The maximum entropy technique (MENT) is used to determine the distribution functions of physical values. MENT naturally combines required maximum entropy, the properties of a system and connection conditions in the form of restrictions…