TY - JOUR
T1 - Quantitative Boltzmann–Gibbs Principles via Orthogonal Polynomial Duality
AU - Ayala Valenzuela, Mario
AU - Carinci, Gioia
AU - Redig, Frank
PY - 2018
Y1 - 2018
N2 - We study fluctuation fields of orthogonal polynomials in the context of particle systems with duality. We thereby obtain a systematic orthogonal decomposition of the fluctuation fields of local functions, where the order of every term can be quantified. This implies a quantitative generalization of the Boltzmann–Gibbs principle. In the context of independent random walkers, we complete this program, including also fluctuation fields in non-stationary context (local equilibrium). For other interacting particle systems with duality such as the symmetric exclusion process, similar results can be obtained, under precise conditions on the n particle dynamics.
AB - We study fluctuation fields of orthogonal polynomials in the context of particle systems with duality. We thereby obtain a systematic orthogonal decomposition of the fluctuation fields of local functions, where the order of every term can be quantified. This implies a quantitative generalization of the Boltzmann–Gibbs principle. In the context of independent random walkers, we complete this program, including also fluctuation fields in non-stationary context (local equilibrium). For other interacting particle systems with duality such as the symmetric exclusion process, similar results can be obtained, under precise conditions on the n particle dynamics.
KW - Boltzmann–Gibbs principle
KW - Duality
KW - Fluctuation field
KW - Orthogonal polynomials
UR - http://www.scopus.com/inward/record.url?scp=85046818882&partnerID=8YFLogxK
UR - http://resolver.tudelft.nl/uuid:60963c9a-3af5-4ce0-beeb-259e30a7b629
U2 - 10.1007/s10955-018-2060-7
DO - 10.1007/s10955-018-2060-7
M3 - Article
SN - 0022-4715
VL - 171
SP - 980
EP - 999
JO - Journal of Statistical Physics
JF - Journal of Statistical Physics
IS - 6
ER -