2006/10/31 by Claudio Castelnovo, Claudio Chamon, . · 1 citation
Mathematics · Physics and Astronomy · #Advanced Thermodynamics and Statistical Mechanics #Combinatorics #Entropy (arrow of time) #Homogeneous space #Mathematics #Opinion Dynamics and Social Influence #Physics #Pure mathematics #Quantum #Quantum many-body systems #Quantum mechanics #Statistical physics #Symmetry protected topological order #Topological entropy #Topological entropy in physics #Topological order #Topological quantum number #Topology (electrical circuits) #cond-mat.stat-mech #cond-mat.str-el
paper · pdf · doi:10.1103/physrevb.76.174416
published as Phys. Rev. B 76, 174416 (2007) · (5 pages, 1 figure) v2: minor changes
openalex publication_date 2007/11/08 · arxiv created 2007/11/09 · arxiv updated 2011/11/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
We show that the concept of topological order, introduced to describe ordered quantum systems which cannot be classified by broken symmetries, also applies to classical systems. We discuss some of the fundamental properties of this type of classical order and propose how to expose it via a generalized topological entropy. Starting from a specific example, we show how to use (quantum) pure state density matrices to construct corresponding (classical) thermally mixed ones that retain precisely half of the original topological entropy, a result that we generalize to a whole class of systems.