Maxent Mechanics
نویسنده
چکیده
This paper shows that: (a) given a mechanical system described by a set of independent coordinates in configuration space, (b) given an initial state of specified initial coordinates, and (c) given a situation in which the system can follow any one of a set of different possible paths with a pertinent probability pi , then the average path (defined as the weighted average positions and corresponding times) will obey Lagranges’ equations iff the Shannon information defined by the distribution of probabilities is an extreme (maximum) compared to any imaginable other distribution. Moreover, the resulting action function is proportional to this Shannon information.
منابع مشابه
Maximum Entropy Production as an Inference Algorithm that Translates Physical Assumptions into Macroscopic Predictions: Don't Shoot the Messenger
Is Maximum Entropy Production (MEP) a physical principle? In this paper I tentatively suggest it is not, on the basis that MEP is equivalent to Jaynes’ Maximum Entropy (MaxEnt) inference algorithm that passively translates physical assumptions into macroscopic predictions, as applied to non-equilibrium systems. MaxEnt itself has no physical content; disagreement between MaxEnt predictions and e...
متن کامل1 A Priori MaxEnt H ( S ) independent class analysis ( ica ) vs
Two mirror symmetric versions of the maximum entropy (MaxEnt) methodology are introduced and compared: (1) A posteriori MaxEnt Independent Component Analysis (ICA) H(V) was proposed by Bell, Sejnowski, Amari, Oja (BSAO) (early by Jutten & Herault, Comon and Cardoso (JHCC) in France). It is ambitious to factorize the unknown joint-probability density function (j-pdf) using the post processing al...
متن کاملSpecies abundance distributions, statistical mechanics and the priors of MaxEnt.
The methods of Maximum Entropy have been deployed for some years to address the problem of species abundance distributions. In this approach, it is important to identify the correct weighting factors, or priors, to be applied before maximising the entropy function subject to constraints. The forms of such priors depend not only on the exact problem but can also depend on the way it is set up; p...
متن کاملMaximum Entropy in Condensed Matter Theory
The principle of maximum entropy has recently been applied to several problems of condensed matter theory. In this paper we discuss some technical aspects of the maxent approach to these problems, and show some general properties of the applications of the method. In particular, we show that maxent can be thought of as a convenient way to close hierarchies, and to extrapolate perturbation serie...
متن کاملA Bayesian Perspective on Markovian Dynamics and the Fluctuation Theorem
One of E. T. Jaynes’ most important achievements was to derive statistical mechanics from the maximum entropy (MaxEnt) method. I re-examine a relatively new result in statistical mechanics, the Evans-Searles fluctuation theorem, from a MaxEnt perspective. This is done in the belief that interpreting such results in Bayesian terms will lead to new advances in statistical physics. The version of ...
متن کاملInferential Scattering
Some di cult conceptual problems that have plagued Statistical Mechanics from the start, are explained by reference to a very simple experiment, which also explains why the MAXENT formalism gives reliable predictions. Then some of the inner workings of MAXENT are revealed by a general perturbation theorem, showing how a prediction is modi ed by adding a new constraint. It is illustrated by the ...
متن کامل