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According to E.T. Jaynes and E.P. Wigner, entropy is an anthropomorphic concept in the sense that in a physical system correspond many thermodynamic systems. The physical system can be examined from many points of view each time examining…
We present a new perspective on the $p$-string condensation procedure for constructing 3+1D fracton phases by implementing this process via the gauging of higher-form symmetries. Specifically, we show that gauging a 1-form symmetry in 3+1D…
We study the dynamics of an open membrane with a cylindrical topology, in the background of a constant three form, whose boundary is attached to p-branes. The boundary closed string is coupled to a two form potential to ensure gauge…
We perform numerical studies including Monte Carlo simulations of high rotational symmetry random tilings. For computational convenience, our tilings obey fixed boundary conditions in regular polygons. Such tilings are put in correspondence…
The angular measure on the unit sphere characterizes the first-order dependence structure of the components of a random vector in extreme regions and is defined in terms of standardized margins. Its statistical recovery is an important step…
In this paper we introduce an alternative localization approach for binary classification that leads to a novel complexity measure: fixed points of the local empirical entropy. We show that this complexity measure gives a tight control over…
We calculate Shannon information entropy of trapped interacting bosons in both the position and momentum spaces, $S_r$ and $S_k$ respectively. The total entropy maintains the fuctional form $S=a + b \ln N$ for repulsive bosons. At the…
During a spontaneous change, a macroscopic physical system will evolve towards a macro-state with more realizations. This observation is at the basis of the Statistical Mechanical version of the Second Law of Thermodynamics, and it provides…
Configurations of fivebranes, twobranes and fourbranes in type IIA string theory, which give (1+1) dimensional supersymmetric gauge theories in the low energy limit, are constructed. It is shown that these brane configurations are…
This paper provides tight bounds on the R\'enyi entropy of a function of a discrete random variable with a finite number of possible values, where the considered function is not one-to-one. To that end, a tight lower bound on the R\'enyi…
We prove a general lower bound of quantum decision tree complexity in terms of some entropy notion. We regard the computation as a communication process in which the oracle and the computer exchange several rounds of messages, each round…
We present a new approach to bootstrapping string-like theories by exploiting a local crossing symmetric dispersion relation and field redefinition ambiguities. This approach enables us to use mass-level truncation and to go beyond the dual…
The confinement of electromagnetic field is studied in axial symmetrical, warped, 6D World Brane, using a recently proposed topological abelian string vortex solution as background. It was found, that the massless gauge field fluctuations…
In three spatial dimensions, particles are limited to either bosonic or fermionic statistics. Two-dimensional systems, on the other hand, can support anyonic quasiparticles exhibiting richer statistical behaviours. An exciting proposal for…
We identify two orthogonal sources of structural entropy in rattler-free granular systems - affine, involving structural changes that only deform the contact network, and topological, corresponding to different topologies of the contact…
Assemblies of allosteric proteins, nano-scale Brownian computers, are the principle information processing devices in biology. The troponin C-troponin I (TnC-TnI) complex, the Ca$^{2+}$-sensitive regulatory switch of the heart, is a…
We present a problem relating measurements and information theory in spin foam models. In the three dimensional case of quantum gravity we can compute probabilities of spin network graphs and study the behaviour of the Shannon entropy…
Depending on context, the term entropy is used for a thermodynamic quantity, a~measure of available choice, a quantity to measure information, or, in the context of statistical inference, a maximum configuration predictor. For systems in…
The rapid scaling of artificial intelligence models has revealed a fundamental tension between model capacity (storage) and inference efficiency (computation). While classical information theory focuses on transmission and storage limits,…
In the first chapter of Shannon's "A Mathematical Theory of Communication," it is shown that the maximum entropy rate of an input process of a constrained system is limited by the combinatorial capacity of the system. Shannon considers…