Related papers: Statistical Physics of Coding for the Integers
We demonstrate that Shannon's information entropy and the thermodynamic entropy of Boltzmann and Gibbs are quantitatively equivalent for real condensed-matter systems. By interpreting atomic configurations as information sources, we compute…
The statistical mechanics of particles that populate indistinguishable energy sub-states is explored. In particular, the mathematical treatment of the microstates differs from conventional statistical mechanics where for a given degeneracy,…
We extend Ziv and Lempel's model of finite-state encoders to the realm of lossy compression of individual sequences. In particular, the model of the encoder includes a finite-state reconstruction codebook followed by an information lossless…
In the canonical formalism of statistical physics, a signature of a first order phase transition for finite systems is the bimodal distribution of an order parameter. Previous thermodynamical studies of nuclear sources produced in heavy-ion…
We study peculiarities of Bose-Einstein condensation of photons that are in thermodynamic equilibrium with atoms of noninteracting gases. General equations of the thermodynamic equilibrium of the system under study are obtained. We examine…
A statistical model for the fragmentation of a conserved quantity is analyzed, using the principle of maximum entropy and the theory of partitions. Upper and lower bounds for the restricted partitioning problem are derived and applied to…
Recent video codecs such as VVC and AV1 apply a Non-rectangular (NR) partitioning to combine prediction signals using a smooth blending around the boundary, followed by a rectangular transform on the whole block. The NR signal…
Compression of integer sets and sequences has been extensively studied for settings where elements follow a uniform probability distribution. In addition, methods exist that exploit clustering of elements in order to achieve higher…
We investigate the overdamped stochastic dynamics of a particle in an asymptotically flat external potential field, in contact with a thermal bath. For an infinite system size, the particles may escape the force field and diffuse freely at…
Cascade solutions of the Boltzmann equation suffer from causality violation at large densities and/or scattering cross sections. Although the particle subdivision technique can reduce the causality violation, it alters event-by-event…
We apply generalized statistical mechanics developed for complex systems to theoretically predict energy spectra of particle and anti-particle degrees of freedom in cosmic ray fluxes, based on a $q$-generalized Hagedorn theory for…
We derive a stochastic process that describes the kinetics of a one-dimensional Bose gas in a regime where three body collisions are important. In this situation the system becomes non integrable offering the possibility to investigate…
If the N bosons that compose an ideal Bose-Einstein gas with energy E and volume V are each assumed to have the average energy of the system E/N, the entropy is easily expressed in terms of the number of bosons N and the number of…
For a system of identical Bose particles sitting on integer energy levels, we give sharp estimates for the convergence of the sequence of occupation numbers to the Bose-Einstein distribution and for the Bose condensation effect.
Universal source coding at short blocklengths is considered for an exponential family of distributions. The \emph{Type Size} code has previously been shown to be optimal up to the third-order rate for universal compression of all memoryless…
There is a class of entropy-coding methods which do not substitute symbols by code words (such as Huffman coding), but operate on intervals or ranges. This class includes three prominent members: conventional arithmetic coding, range…
Compression also known as entropy coding has a rich and long history. However, a recent explosion of multimedia Internet applications (such as teleconferencing and video streaming for instance) renews an interest in fast compression that…
In this paper, we mainly review recent results on mathematical theory and numerical methods for Bose-Einstein condensation (BEC), based on the Gross-Pitaevskii equation (GPE). Starting from the simplest case with one-component BEC of the…
We calculate certain features of Bose-Einstein condensation in the ideal gas by using recurrence relations for the partition function. The grand canonical ensemble gives inaccurate results for certain properties of the condensate that are…
Abstract: In this article, we will analyze in detail the coding limit of an individual sequence by introducing the latest developments brought by the Set Shaping Theory. This new theory made us realize that there is a huge difference…