Related papers: Statistical Physics of Coding for the Integers
We discuss statics and dynamics of condensation in a zero-range process with compartments of limited sizes. For the symmetric dynamics the stationary state has a factorized form. For the asymmetric dynamics the steady state factorizes only…
It is shown that the grand partition function of an ideal Bose system with single particle spectrum $\epsilon_i = (2n+k+3/2)\hbar\omega$ is identical to that of a system of particles with single particle energy $\epsilon_i…
We show how universal codes can be used for solving some of the most important statistical problems for time series. By definition, a universal code (or a universal lossless data compressor) can compress any sequence generated by a…
The issue of the thermodynamics of a system of distinguishable particles is discussed in this paper. In constructing the statistical mechanics of distinguishable particles from the definition of Boltzmann entropy, it is found that the…
Equilibrium statistics of Hamiltonian systems is correctly described by the microcanonical ensemble. Classically this is the manifold of all points in the N-body phase space with the given total energy. Due to Boltzmann's principle,…
In this paper we will analyze discrete probability distributions in which probabilities of particular outcomes of some experiment (microstates) can be represented by the ratio of natural numbers (in other words, probabilities are…
We introduce a universal quantization scheme based on random coding, and we analyze its performance. This scheme consists of a source-independent random codebook (typically_mismatched_ to the source distribution), followed by optimal…
An explicit calculation is given of the entropy/energy ratio for the TM modes of the electromagnetic field in the half Einstein universe. This geometry provides a mathematically convenient and physically instructive example of how the…
This article presents a study of the grand canonical Bose-Einstein (BE) statistics for a finite number of particles in an arbitrary quantum system. The thermodynamical quantities that identify BE condensation -- namely, the fraction of…
Text compression schemes and compact data structures usually combine sophisticated probability models with basic coding methods whose average codeword length closely match the entropy of known distributions. In the frequent case where basic…
All of the thermodynamic information on a statistical mechanical system is encoded in the locus and density of its partition function zeroes. Recently, a new technique was developed which enables the extraction of the latter using…
To test a possible relation between the topological entropy and the Arnold complexity, and to provide a non trivial example of a rational dynamical zeta function, we introduce a two-parameter family of two-dimensional discrete rational…
The order statistics based list decoding techniques for linear binary block codes of small to medium block length are investigated. The construction of the list of the test error patterns is considered. The original order statistics…
We consider a system composed of a fixed number of particles with total energy smaller or equal to some prescribed value. The particles are non-interacting, indistinguishable and distributed over fixed number of energy levels. The energy…
This paper considers the problem of data compression for dependent quantum systems. It is the second in a series under the same title. As in the previous paper, we are interested in Lempel--Ziv encoding for quantum Gibbs ensembles. Here, we…
In prefix coding over an infinite alphabet, methods that consider specific distributions generally consider those that decline more quickly than a power law (e.g., Golomb coding). Particular power-law distributions, however, model many…
An ensemble of classical subsystems interacting with surrounding particles has been considered. In general case, a phase volume of the subsystems ensemble was shown to be a function of time. The evolutional equations of the ensemble are…
Equilibrium statistics of Hamiltonian systems is correctly described by the microcanonical ensemble. Classically this is the manifold of all points in the $N-$body phase space with the given total energy. Due to Boltzmann's principle,…
We optimize number squeezing when splitting a mesoscopic Bose Einstein condensate. Applying optimal control theory to a realistic description of the condensate allowed us to identify a form of the splitting ramp which drastically…
It is well known that the mathematically accurate description of ordering and related symmetry breaking in statistical systems requires to consider the thermodynamic limit. But the order does not appear from nowhere, and yet before the…