2009/07/31 by Vladimir Y. Chernyak, Michael Chertkov, Sergey V. Malinin +1 · 1 citation
Physics and Astronomy · #Advanced Thermodynamics and Statistical Mechanics #Context (archaeology) #Current (fluid) #Large deviations theory #Morse theory #Quantum many-body systems #Theoretical and Computational Physics #Topological entropy in physics #Topological quantum number #Topology (electrical circuits) #cond-mat.dis-nn #cond-mat.stat-mech
paper · pdf · doi:10.1007/s10955-009-9832-z
published as J.Stat.Phys.137:1,2009 · 30 pages, 4 figures
arxiv created 2009/09/13 · openalex publication_date 2009/09/29 · arxiv updated 2015/05/13 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
In many experimental situations, a physical system undergoes stochastic evolution which may be described via random maps between two compact spaces. In the current work, we study the applicability of large deviations theory to time-averaged quantities which describe such stochastic maps, in particular time-averaged currents and density functionals. We derive the large deviations principle for these quantities, as well as for global topological currents, and formulate variational, thermodynamic relations to establish large deviation properties of the topological currents. We illustrate the theory with a nontrivial example of a Heisenberg spin-chain with a topological driving of the Wess-Zumino type. The Cramér functional of the topological current is found explicitly in the instanton gas regime for the spin-chain model in the weak-noise limit. In the context of the Morse theory, we discuss a general reduction of continuous stochastic models with weak noise to effective Markov chains describing transitions between stable fixed points.