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Article
Optics
Paul M. Alsing et al.
Summary: In this paper, the authors discuss the relation between the Sjoqvist metric and the Bures metric for mixed quantum states using decompositions of density operators by means of ensembles of pure quantum states. They compare the formal expressions of these metrics for thermal quantum states and illustrate the difference between them in a simple physical system. Finally, the Bures and Sjoqvist metrics are compared in terms of their monotonicity property.
Article
Physics, Multidisciplinary
Carlo Cafaro et al.
Summary: Thermodynamic length is a metric distance that quantifies the dissipation induced by a finite time transformation of a thermodynamic system. By studying thermodynamic length, the departures between real gases and ideal gases are evaluated, and a strategy is proposed to relate thermodynamic lengths to the efficiency of thermodynamic systems. Furthermore, the efficiency is used to distinguish ideal and non-ideal thermal behaviors and quantify deviations from ideality for various real gases.
PHYSICA A-STATISTICAL MECHANICS AND ITS APPLICATIONS
(2022)
Article
Astronomy & Astrophysics
Carlo Cafaro et al.
Summary: This paper proposes an information geometric theoretical construct to describe and understand the complex behavior of evolutions of quantum systems in pure and mixed states. By comparing and analyzing different metrics, the study finds that the evolution of mixed quantum states is more complex and verifies the effectiveness of the proposed measure of complexity in ranking. Additionally, the paper observes a softening of complexity on the Bures manifold compared to the Sjoqvist manifold.
Article
Materials Science, Multidisciplinary
Bruno Mera et al.
Summary: This study analyzes the thermodynamical limit of the quantum metric along critical submanifolds of theory space. It relates the singular behavior of the metric to normal directions using the language of information theory and differential geometry.
Article
Physics, Fluids & Plasmas
Carlo Cafaro et al.
Summary: In this research, an information geometric characterization of quantum driving schemes is presented, focusing on su(2; C ) time-dependent Hamiltonians, complexity, and efficiency concepts. The study analyzes the probability paths and investigates the optimum paths and minimum entropy production. Evaluations based on information geometric complexity and a newly proposed measure of entropic efficiency provide rankings for different driving schemes.
Article
Physics, Multidisciplinary
Tan Van Vu et al.
Summary: In this study, geometrical bounds on irreversibility in quantum and classical Markovian open systems satisfying the detailed balance condition were derived using information geometry. It was proven that irreversible entropy production is constrained by a modified Wasserstein distance between initial and final states, enhancing the Clausius inequality in reversible-Markov systems. These bounds, interpreted as quantum and classical speed limits, constrain the minimum time required for transforming a system state, and can be used to obtain tighter efficiency bounds for quantum heat engines.
PHYSICAL REVIEW LETTERS
(2021)
Article
Physics, Mathematical
Steven Gassner et al.
Summary: In this study, an information geometric analysis of entropic speeds and entropy production rates in pure quantum states was conducted, showing that the shortest path corresponds to minimal entropy production, and a faster transfer speed is associated with a higher rate of entropy production.
INTERNATIONAL JOURNAL OF GEOMETRIC METHODS IN MODERN PHYSICS
(2021)
Article
Physics, Multidisciplinary
Pedro Pessoa et al.
Summary: Information geometry is a branch of probability theory that assigns a Riemannian differential geometry structure to the space of probability distributions. This study investigates the information geometry of gases following Fermi-Dirac and Bose-Einstein quantum statistics, computing the Fisher-Rao information metric and scalar curvature. Analyzing the ground state of the ideal bosonic gas reveals the disappearance of the singular behavior of curvature in the condensation region, which contradicts a long-held conjecture about curvature divergence in phase transitions.
PHYSICA A-STATISTICAL MECHANICS AND ITS APPLICATIONS
(2021)
Article
Materials Science, Multidisciplinary
Hector Silva et al.
Summary: The paper introduces a natural extension of a Riemannian structure, initially introduced in the space of nondegenerate density matrices, to the case of eigenspaces with dimension greater than or equal to 1. A physical interpretation of the metric in terms of interferometric measurement is presented, and it is applied to study topological phase transitions in band insulators at finite temperatures. A comparison of this metric and the well-known Bures metric shows significantly different behaviors, with the former predicting finite-temperature phase transitions in addition to zero-temperature transitions. The differences in behaviors are attributed to a symmetry-breaking mechanism, similar to Landau-Ginzburg theory, which breaks down the Uhlmann gauge group into a subgroup based on the system's density matrix type.
Article
Physics, Multidisciplinary
Kay Brandner et al.
PHYSICAL REVIEW LETTERS
(2020)
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Harry J. D. Miller et al.
PHYSICAL REVIEW LETTERS
(2020)
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Physics, Multidisciplinary
Sosuke Ito et al.
PHYSICAL REVIEW RESEARCH
(2020)
Article
Physics, Multidisciplinary
Erik Sjoqvist
PHYSICAL REVIEW RESEARCH
(2020)
Article
Physics, Multidisciplinary
Carlo Cafaro et al.
EUROPEAN PHYSICAL JOURNAL PLUS
(2020)
Article
Physics, Fluids & Plasmas
Carlo Cafaro et al.
Article
Physics, Multidisciplinary
Dorje C. Brody et al.
PHYSICAL REVIEW RESEARCH
(2019)
Review
Mathematics, Applied
Domenico Felice et al.
Article
Materials Science, Multidisciplinary
B. Karimi et al.
Review
Multidisciplinary Sciences
M. H. Devoret et al.
Article
Mathematics, Interdisciplinary Applications
Carlo Cafaro
CHAOS SOLITONS & FRACTALS
(2009)
Article
Physics, Multidisciplinary
F. G. Paauw et al.
PHYSICAL REVIEW LETTERS
(2009)
Review
Multidisciplinary Sciences
John Clarke et al.
Article
Optics
Paolo Zanardi et al.
Article
Materials Science, Multidisciplinary
A. O. Niskanen et al.
Article
Physics, Multidisciplinary
Paolo Zanardi et al.
PHYSICAL REVIEW LETTERS
(2007)
Article
Multidisciplinary Sciences
I Chiorescu et al.
