Special Issue "Symmetry and Symmetry Breaking in Statistical Systems"

A special issue of Symmetry (ISSN 2073-8994).

Deadline for manuscript submissions: closed (30 November 2015).

Special Issue Editor

Prof. Dr. Purushottam D. Gujrati
E-Mail Website
Guest Editor
1. Department of Physics, The University of Akron, Akron, OH 44325, USA
2. Department of Polymer Science, The University of Akron, Akron, OH 44325, USA
Interests: phase transitions and critical phenomena; non-equilibrium statistical thermodynamics; bulk and confined space thermodynamics; polymer physics; solution theory; combinatorics and graph theory; renormalization group and field theory
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Special Issue Information

Dear Colleagues,

Background: How things change in nature is controlled by two separate factors: the initial conditions, which may be unpredictable, and the laws that synthesize the regularity, but may be hard to discover because of irregularities produced by uncontrollable external factors. It is in the discovery of laws that symmetry principles play a crucial role. As external factors are central to statistical systems, symmetry principles also play an important role. Gibbs had already realized the importance of permutation symmetry in clarifying the paradox named after him. The symmetry principles of physical laws are modified by the statistics of large systems and determine the properties of the latter. While the role of symmetry principles in equilibrium statistical mechanics has been understood for quite some time, their role in non-equilibrium statistical physics is just as important, as is evidenced by Onsager’s reciprocity relations and by the Curie symmetry principle; the latter immediately leads to the idea of symmetry breaking, which permeates the entire field of statistical physics. Accordingly, while the basic laws governing a system have certain symmetries, some or all of them need not be present in the observed behavior. Despite this, the missing symmetries have consequences for the system, such as the emergence of Goldstone bosons (phonons, magnons, pions, etc.) and control phase transitions. In addition, new symmetries, such as scale invariance, can emerge thermodynamically near a critical point.

Scope: The symmetry principles (global or local as in gauge symmetries) should, in general, control the static and dynamic properties of all statistical systems including, but not limited to, equilibrium phases, phase transitions (classical and quantum), non-equilibrium states, transport, distinction between heat and work, fluctuations close to or far from equilibrium, quantum systems (closed or open), nature of coarse graining, topological phases, etc.

Recent Trends: Recently, symmetry operations have been used in identifying entangled states to better understand quantum phase transitions. In addition, considerable attention has been paid to understanding the consequences of symmetry on entanglement between a system and the surrounding medium as part of developing the principles of quantum thermodynamics. Another recent field of activity relates to various fluctuation theorems, which strongly constrain the nature of far from equilibrium fluctuations. As the fluctuations are governed by the Hamiltonian dynamics, which operate at the microscopic level, the symmetry of the Hamiltonian must also have ramifications for the fluctuations. Stochastic thermodynamics exploiting microstate evolution is another active field being pursued recently. There has been some effort to microscopically explain heat and work in terms of microstates. The application of AdS/CFT to conformal field theories has also received attention in string theory and model systems near a critical point.

Aim: My hope is to have contributions on various symmetries, those that are part of laws and those that are generated thermodynamically (also called dynamically), such as near a second order phase transition, in classical and quantum statistical physics applied to condensed matter, particle physics, black hole thermodynamics, etc., to provide a comprehensive perspective of the usefulness of symmetry principles, including recent cutting-edge trends, some of which are noted above.

Prof. Dr. Purushottam D. Gujrati
Guest Editor

Manuscript Submission Information

Manuscripts should be submitted online at www.mdpi.com by registering and logging in to this website. Once you are registered, click here to go to the submission form. Manuscripts can be submitted until the deadline. All papers will be peer-reviewed. Accepted papers will be published continuously in the journal (as soon as accepted) and will be listed together on the special issue website. Research articles, review articles as well as short communications are invited. For planned papers, a title and short abstract (about 100 words) can be sent to the Editorial Office for announcement on this website.

Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere (except conference proceedings papers). All manuscripts are thoroughly refereed through a single-blind peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Symmetry is an international peer-reviewed open access monthly journal published by MDPI.

Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 1800 CHF (Swiss Francs). Submitted papers should be well formatted and use good English. Authors may use MDPI's English editing service prior to publication or during author revisions.

Keywords

  • space group symmetries,
  • time-reversal symmetry,
  • permutation,
  • liquid crystal symmetries,
  • scale invariance,
  • conformal invariance,
  • gauge symmetry,
  • supersymmetry,
  • chiral symmetry,
  • symmetry breaking and restoration,
  • material frame indifference and covariance transformation;
  • heat and work,
  • adiabatic invariance,
  • temperature in relativistic thermodynamics,
  • entanglement,
  • fluctuation theorems,
  • stochastic thermodynamics,
  • quantum thermodynamics,
  • black hole thermodynamics;
  • holographic principle;
  • AdS/CFT

Published Papers (3 papers)

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Research

Article
On Consistent Nonparametric Statistical Tests of Symmetry Hypotheses
Symmetry 2016, 8(5), 31; https://doi.org/10.3390/sym8050031 - 06 May 2016
Cited by 5 | Viewed by 1950
Abstract
Being able to formally test for symmetry hypotheses is an important topic in many fields, including environmental and physical sciences. In this paper, one concentrates on a large family of nonparametric tests of symmetry based on Cramér–von Mises statistics computed from empirical distribution [...] Read more.
Being able to formally test for symmetry hypotheses is an important topic in many fields, including environmental and physical sciences. In this paper, one concentrates on a large family of nonparametric tests of symmetry based on Cramér–von Mises statistics computed from empirical distribution and characteristic functions. These tests possess the highly desirable property of being universally consistent in the sense that they detect any kind of departure from symmetry as the sample size becomes large. The asymptotic behaviour of these test statistics under symmetry is deduced from the theory of first-order degenerate V-statistics. The issue of computing valid p-values is tackled using the multiplier bootstrap method suitably adapted to V-statistics, yielding elegant, easy-to-compute and quick procedures for testing symmetry. A special focus is put on tests of univariate symmetry, bivariate exchangeability and reflected symmetry; a simulation study indicates the good sampling properties of these tests. Finally, a framework for testing general symmetry hypotheses is introduced. Full article
(This article belongs to the Special Issue Symmetry and Symmetry Breaking in Statistical Systems)
Article
A Combinatorial Approach to Time Asymmetry
Symmetry 2016, 8(3), 11; https://doi.org/10.3390/sym8030011 - 15 Mar 2016
Cited by 3 | Viewed by 1881
Abstract
In this paper, simple models for the multiverse are analyzed. Each universe is viewed as a path in a graph, and by considering very general statistical assumptions, essentially originating from Boltzmann, we can make the set of all such paths into a finite [...] Read more.
In this paper, simple models for the multiverse are analyzed. Each universe is viewed as a path in a graph, and by considering very general statistical assumptions, essentially originating from Boltzmann, we can make the set of all such paths into a finite probability space. We can then also attempt to compute the probabilities for different kinds of behavior and in particular under certain conditions argue that an asymmetric behavior of the entropy should be much more probable than a symmetric one. This offers an explanation for the asymmetry of time as a broken symmetry in the multiverse. The focus here is on simple models which can be analyzed using methods from combinatorics. Although the computational difficulties rapidly become enormous when the size of the model grows, this still gives hints about how a full-scale model should behave. Full article
(This article belongs to the Special Issue Symmetry and Symmetry Breaking in Statistical Systems)
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Article
Polarity Formation in Molecular Crystals as a Symmetry Breaking Effect
Symmetry 2016, 8(3), 10; https://doi.org/10.3390/sym8030010 - 11 Mar 2016
Cited by 7 | Viewed by 1992
Abstract
The transition of molecular crystals into a polar state is modeled by a one-dimensional Ising Hamiltonian in multipole expansion and a suitable order parameter. Two symmetry breakings are necessary for the transition: the translational and the spin flip invariance—the former being broken by [...] Read more.
The transition of molecular crystals into a polar state is modeled by a one-dimensional Ising Hamiltonian in multipole expansion and a suitable order parameter. Two symmetry breakings are necessary for the transition: the translational and the spin flip invariance—the former being broken by geometric constraints, the latter by the interaction of the first non-zero multipole with the next order multipole. Two different behaviors of the thermal average of the order parameter as a function of position are found. The free energy per lattice site converges to a finite value in the thermodynamic limit showing the consistency of the model in a macroscopic representation. Full article
(This article belongs to the Special Issue Symmetry and Symmetry Breaking in Statistical Systems)
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