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arXiv2007

The Physics of Information

We review of the interface between (theoretical) physics and information for non-experts. The origin of information as related to the notion of entropy is described, first in the context of thermodynamics then in the context of statistical mechanics. A close examination of the foundations of statistical mechanics and the need to reconcile the probabilistic and deterministic views of the world leads us to a discussion of chaotic dynamics, where information plays a crucial role in quantifying predictability. We then discuss a variety of fundamental issues that emerge in defining information and how one must exercise care in discussing concepts such as order, disorder, and incomplete knowledge. We also discuss an alternative form of entropy and its possible relevance for nonequilibrium thermodynamics. In the final part of the paper we discuss how quantum mechanics gives rise to the very different concept of quantum information. Entirely new possibilities for information storage and computation are possible due to the massive parallel processing inherent in quantum mechanics. We also point out how entropy can be extended to apply to quantum mechanics to provide a useful measurement for quantum entanglement. Finally we make a small excursion to the interface betweeen quantum theory and general relativity, where one is confronted with an "ultimate information paradox" posed by the physics of Black Holes. In this review we have limited ourselves; not all relevant topics that touch on physics and information could be covered.

physics.class-ph↗
arXiv2008

Path to finding the critical thickness for memory in thin ferroelectric films

The finite screening length by real metallic electrodes, albeit very small (<1A), results in finite depolarizing field that tends to split the film into domains. In very thin ferroelectric films the domain structure reduces to sinusoidal distribution of polarization considered first in the 1980s. We discuss the phase transition between this structure and a single domain state and show that it is first order, if it exists at all. The alternative possibility is that the single domain state at zero bias voltage would be metastable for all temperatures in most systems. This scenario defines a path towards solution to a problem of finding parameters of a system that can sustain the ferroelectric memory over a desired period of time.

cond-mat.mtrl-sci↗
arXiv2009

On causally asymmetric versions of Occam's Razor and their relation to thermodynamics

In real-life statistical data, it seems that conditional probabilities for the effect given their causes tend to be less complex and smoother than conditionals for causes, given their effects. We have recently proposed and tested methods for causal inference in machine learning using a formalization of this principle. Here we try to provide some theoretical justification for causal inference methods based upon such a ``causally asymmetric'' interpretation of Occam's Razor. To this end, we discuss toy models of cause-effect relations from classical and quantum physics as well as computer science in the context of various aspects of complexity. We argue that this asymmetry of the statistical dependences between cause and effect has a thermodynamic origin. The essential link is the tendency of the environment to provide independent background noise realized by physical systems that are initially uncorrelated with the system under consideration rather than being finally uncorrelated. This link extends ideas from the literature relating Reichenbach's principle of the common cause to the second law.

cond-mat.stat-mech↗
arXiv2008

Modeling polymerization of microtubules: a quantum mechanical approach

In this paper a quantum mechanical description of the assembly/disassembly process for microtubules is proposed. We introduce creation and annihilation operators that raise or lower the microtubule length by a tubulin layer. Following that, the Hamiltonian and corresponding equations of motion for the quantum fields are derived that describe the dynamics of microtubules. These Heisenberg-type equations are then transformed to semi-classical equations using the method of coherent structures. We find that the dynamics of a microtubule can be mathematically expressed via a cubic-quintic nonlinear Schrödinger (NLS) equation. We show that a vortex filament, a generic solution of the NLS equation, exhibits linear growth/shrinkage in time as well as temporal fluctuations about some mean value which is qualitatively similar to the dynamic instability of microtubules.

q-bio.BM↗
arXiv2007

Correlation function of the two-dimensional Ising model on a finite lattice. II

We calculate the two-point correlation function and magnetic susceptibility in the anisotropic 2D Ising model on a lattice with one infinite and the other finite dimension, along which periodic boundary conditions are imposed. Using exact expressions for a part of lattice form factors, we propose the formulas for arbitrary spin matrix elements, thus providing a possibility to compute all multipoint correlation functions in the anisotropic Ising model on cylindrical and toroidal lattices. The scaling limit of the corresponding expressions is also analyzed.

nlin.SI↗
arXiv2007

Specific heat of the mixed spin-1/2 and spin-S Ising model with a rope ladder structure

The mixed spin-1/2 and spin-S (S>1/2) Ising model on a rope ladder is examined by combining two exact analytical methods. By the decoration-iteration mapping transformation, this mixed-spin system is firstly transformed to a simple spin-1/2 Ising model on the two-leg ladder, which is then exactly solved by the standard transfer-matrix method. The thermal variations of the zero-field specific heat are discussed in particular.

cond-mat.stat-mech↗
arXiv2007

The spin-1/2 Ising model on the bow-tie lattice as an exactly soluble free-fermion model

The spin-1/2 Ising model on the bow-tie lattice is exactly solved by establishing a precise mapping relationship with its corresponding free-fermion eight-vertex model. Ground-state and finite-temperature phase diagrams are obtained for the anisotropic bow-tie lattice with three different exchange interactions along three different spatial directions.

cond-mat.stat-mech↗
arXiv2007

Confining vacua and Q-state Potts models with Q<1

In most Yang-Mills models the vacuum where magnetic monopoles condense coincides with that where center vortices percolate, thus it is not clear which of these two properties is most directly involved in producing confinement. It is pointed out that there is a class of 3D gauge models, which can be though of as duals of Q-state Potts models with Q < 1, where the magnetic monopole condensation is a necessary but not sufficient condition for percolation of center vortices. A set of numerical tests at Q=1/10 shows that there is a vacuum in which the magnetic monopole condensate does not yield confinement, in the sense that large Wilson loops obey a perimeter law. In such a vacuum the center vortices form a dilute gas of loops. At stronger coupling there is also a truly confining vacuum where both confining mechanisms are present.

hep-lat↗
arXiv2008

Generalized Quantum Hydrodynamics and Principles of non-Local Physics

This paper addresses the fundamental principles of generalized Boltzmann physical kinetics, as a part of non-local physics. It is shown that the theory of transport processes (including quantum mechanics) can be considered in the frame of unified theory based on the non-local physical description. The paper can be considered also as comments and prolongation of the materials published in the known author's monograph (Boris V. Alexeev, Generalized Boltzmann Physical Kinetics. Elsevier. 2004).

cond-mat.stat-mech↗
arXiv2007

Estimating the size of the solution space of metabolic networks

In this work we propose a novel algorithmic strategy that allows for an efficient characterization of the whole set of stable fluxes compatible with the metabolic constraints. The algorithm, based on the well-known Bethe approximation, allows the computation in polynomial time of the volume of a non full-dimensional convex polytope in high dimensions. The result of our algorithm match closely the prediction of Monte Carlo based estimations of the flux distributions of the Red Blood Cell metabolic network but in incomparably shorter time. We also analyze the statistical properties of the average fluxes of the reactions in the E-Coli metabolic network and finally to test the effect of gene knock-outs on the size of the solution space of the E-Coli central metabolism.

cond-mat.dis-nn↗
arXiv2007

Computing quantum phase transitions

This article first gives a concise introduction to quantum phase transitions, emphasizing similarities with and differences to classical thermal transitions. After pointing out the computational challenges posed by quantum phase transitions, a number of successful computational approaches is discussed. The focus is on classical and quantum Monte Carlo methods, with the former being based on the quantum-to classical mapping while the latter directly attack the quantum problem. These methods are illustrated by several examples of quantum phase transitions in clean and disordered systems.

cond-mat.stat-mech↗
arXiv2008

Maximum Entropy Principle for the Microcanonical Ensemble

We derive the microcanonical ensemble from the Maximum Entropy Principle (MEP) using the phase space volume entropy of P. Hertz. Maximizing this entropy with respect to the probability distribution with the constraints of normalization and average energy, we obtain the condition of constant energy. This approach is complementary to the traditional derivation of the microcanonical ensemble from the MEP using Shannon entropy and assuming a priori that the energy is constant which results in equal probabilities.

cond-mat.stat-mech↗
arXiv2008

Fermi-point scenario for emergent gravity

Let us assume that gravity is an emergent low-energy phenomenon arising from a topologically stable defect in momentum space -- the Fermi point. What are the consequences? We discuss the natural values of fermion masses and cosmological constant; flatness of the Universe; bounds on Lorentz violation; etc.

gr-qc↗
arXiv2007

Higher order terms in the condensate fraction of a homogeneous and dilute Bose gas

The condensate fraction of a homogeneous and dilute Bose gas is expanded as a power series of $\sqrt{n a^3}$ as $N_0/N = 1 -c_1 (n a^3)^{1/2} -c_2 (n a^3) - c_3 (n a^3)^{3/2}\hdots.$ The coefficient $c_1$ is well-known as $8/3 \sqrtπ$, but the others are unknown yet. Considering two-body contact interactions and applying a canonical transformation method twice we developed the method to obtain the higher order coefficients analytically. An iteration method is applied to make up a cutoff in a fluctuation term. The coefficients ares $c_2=2(π- 8/3)$ and $c_3=(4/\sqrtπ) (π-8/3)(10/3-π)$.

cond-mat.stat-mech↗
arXiv2007

Combinatorics of the Dimer Model on a Strip

In this note, we give a closed formula for the partition function of the dimer model living on a (2 x n) strip of squares or hexagons on the torus for arbitrary even n. The result is derived in two ways, by using a Potts model like description for the dimers, and via a recursion relation that was obtained from a map to a 1D monomer-dimer system. The problem of finding the number of perfect matchings can also be translated to the problem of finding a minmal feedback arc set on the dual graph.

math.CO↗
arXiv2007

Spiral growth, two-dimensional nucleation, and the Ehrlich-Schwoebel effect

Frank's prediction of the spiral growth mode in 1949 defined a pivotal moment in the history of crystal growth. In recent decades the topic has received less attention, and instead we have seen a resurrection of two-dimensional nucleation theory in the context of growth experiments on defect-free homoepitaxial thin films. In particular, the key role of interlayer transport controlled by step edge barriers of the Ehrlich-Schwoebel type in shaping the morphology of multilayer films has been increasingly recognized. After a brief review of the classical theory, this paper reports on a recent study of spiral growth in the presence of step edge barriers. Our key observation is that step edge barriers lead to unconventionally shaped spiral hillocks that display the same characteristic ever-steepening height profiles as wedding cakes formed during growth by two-dimensional nucleation. This prediction was verified experimentally by inducing screw dislocations through ion bombardment of the Pt(111) surface, thus creating a homoepitaxial growth system on which spiral hillocks and wedding cakes coexist.

cond-mat.mtrl-sci↗
arXiv2009

Markov Chain Hidden behind Power Law Mechanism of Self-organized Criticality

To describe and analyze the dynamics of Self-Organized Criticality (SOC) systems, a four-state continuous-time Markov model is proposed in this paper. Different to computer simulation or numeric experimental approaches commonly employed for explaining the power law in SOC, in this paper, based on this Markov model, using E.T.Jayness' Maximum Entropy method, we have derived a mathematical proof on the power law distribution for the size of these events. Both this Makov model and the mathematical proof on power law present a new angle on the universality of power law distributions, they also show that the scale free property exists not necessary only in SOC system, but in a class of dynamical systems which can be modelled by the proposed Markov model.

cond-mat.stat-mech↗