Large-deviations limits for non-equilibrium Markov processes, path entropies, and applications
Document Type
Presentation Abstract
Presentation Date
10-14-2013
Abstract
A variety of methods now exist, some developed over the past 40 years in statistical physics, to compute large-deviation functions for non- equilibrium Markovian stochastic processes. More important than technical methods is the understanding that these functions define the relevant notions of entropy and thermodynamic limits for systems both at and away from equilibrium, in domains ranging from mechanics to inference. Much of the richness of non-equilibrium large- deviations theory is being developed in systems chemistry, cell and molecular biology, and population processes, because these combine features of intermediate numbers of degrees of freedom and complex state-space structure that make fluctuations both important and challenging to compute. I will sketch key concepts and some methods for modern non-equilibrium large-deviations theory, and present a collection of examples from cell and population biology showing the use of symmetry and collective fluctuations as organizing concepts, and the appropriate role of entropy corrections in fundamentally non- equilibrium systems. I will close with some future areas of opportunity particularly in molecular biology and possibly microbial ecology.
Recommended Citation
Smith, D. Eric, "Large-deviations limits for non-equilibrium Markov processes, path entropies, and applications" (2013). Colloquia of the Department of Mathematical Sciences. 437.
https://scholarworks.umt.edu/mathcolloquia/437
Additional Details
Monday, October 14 at 3:10 p.m. in Math 103