Entropy In Statistical Mechanics Research Articles

A lattice field theory for polymer systems with nearest-neighbor interaction energies

We generalize a lattice field theory that formally provides an exact description of the statistical mechanical entropy of nonoverlapping flexible polymers to enable treatment of nearest-neighbor interaction energies. The theory is explicitly solved within an extended mean field approximation for a system of polymer chains and voids, and we also provide mean field results for polymer–solvent–void and binary blend–void mixtures. In addition to recovering the Flory–Huggins mean field approximation for these systems, our extended definition of the mean field approximation contains a set of corrections to Flory–Huggins theory in the form of an expansion in powers of the nearest-neighbor interaction energies.

On coarse‐grained entropy and mixing in statistical mechanics

The object of the paper If the study the roles of non‐equillbrium entropy and mixing of phases in the statistical characterization of the coarse‐grained interpretation of the irreversible approach to statistical equilibrlum of an isolated system.

Mathematics of switching processes with applications to squash and statistical mechanics

A switching process is defined as one where a number of organizations compete for a sequence of rewards, the probability of any organization gaining a particular reward depending on whether it gained the previous reward. An example is the game of squash, where a player may only gain points when serving, the service being transferred only when the server loses a rally. This game is analysed fairly completely. An analogy is developed between this type of statistics, and that involved in the concept of entropy in statistical mechanics.

The Application of Entropy to the Measurement of Social and Economic Freedom

This study was inspired by the concept of entropy as applied to the measurement of the extent of information in the communication theory of Wiener and Shannon. Like its precursor, entropy in statistical mechanics, it is a convenient measure of the uncertainty or unpredictability of a system or of a process containing an element of contingency. By keeping in mind the fact that in human circles unpredictability is often allowed to pass under the sacred name of liberty, it is possible to perceive an opening for mathematics into a domain which was until now inaccessible to the mathematician. It was four years ago that we made a first attempt to enter that field in our “Essay on the Mathematical Theory of Freedom”, presented to the Royal Statistical Society of London.

The conditional entropy in the microcanonical ensemble

The existence of the configurational microcanonical conditional entropy in classical statistical mechanics is proved in the thermodynamic limit for a class of long-range multiparticle observables. This result generalizes a theorem of Lanford for finite range observables.

A possible derivation of configurational entropy of binary alloys from diffuse scattering observations

A representation of statistical ensemble for a binary alloy is shown obtainable by observing the diffuse scattering amplitudes, which enables us to evaluate the configurational entropy of the system from the very definition of entropy in statistical mechanics.

Sorting, trees, and measures of order

This paper analyses the best methods of sorting on a digital computer. Two main types, “sorting by merging” and “distribution sorting” are considered. The strategy to be used is diagrammed by a tree. Optimum strategy is shown to depend on the order already existing in the data. Given this, a minimal tree is constructed giving the best strategy. A relation is shown between distribution sorting and decoding a set of messages, or searching for a particular message on a list. Two criteria for pre-existing order among items are established, and measures of order and disorder are defined. Analogy is shown between a measure of disorder and entropy in statistical mechanics, and between a measure of order and a measure of information.

The concept of parsimony in factor analysis

The concept of parsimony in factor analysis is discussed. Arguments are advanced to show that this concept bears an analogic relationship to entropy in statistical mechanics and information in communication theory. A formal explication of the term parsimony is proposed which suggests approaches to the final resolution of the rotational problem. This paper provides the rationale underlying Carroll's (2) analytical solution for approximating simple structure, and the solutions of Saunders (7) and Neuhaus and Wrigley (5).