scholarly journals Entropic Distance for Nonlinear Master Equation

Universe ◽  
2018 ◽  
Vol 4 (1) ◽  
pp. 10 ◽  
Author(s):  
Tamás Biró ◽  
András Telcs ◽  
Zoltán Néda
Keyword(s):  
Master Equation ◽  
Entropic Distance ◽  
Nonlinear Master Equation

An asymptotic expansion of the nonlinear master equation

1977 ◽  
Vol 16 (2) ◽  
pp. 201-215 ◽  
Author(s):  
W. Horsthemke ◽  
M. Malek-Mansour ◽  
B. Hayez
Keyword(s):  
Asymptotic Expansion ◽  
Master Equation ◽  
Nonlinear Master Equation

scholarly journals Information geometry, trade-off relations, and generalized Glansdorff-Prigogine criterion for stability

2021 ◽  
Author(s):  
Sosuke Ito
Keyword(s):  
Master Equation ◽  
Entropy Production ◽  
Production Rate ◽  
Excess Entropy ◽  
Information Geometry ◽  
Entropy Production Rate ◽  
Trade Off ◽  
Geometric Criterion ◽  
Excess Entropy Production ◽  
Nonlinear Master Equation

Abstract We discuss a relationship between information geometry and the Glansdorff-Prigogine criterion for stability. For the linear master equation, we found a relation between the line element and the excess entropy production rate. This relation leads to a new perspective of stability in a nonequilibrium steady-state. We also generalize the Glansdorff-Prigogine criterion for stability based on information geometry. Our information-geometric criterion for stability works well for the nonlinear master equation, where the Glansdorff-Prigogine criterion for stability does not work well. We derive a trade-off relation among the fluctuation of the observable, the mean change of the observable, and the intrinsic speed. We also derive a novel thermodynamic trade-off relation between the excess entropy production rate and the intrinsic speed. These trade-off relations provide a physical interpretation of our information-geometric criterion for stability. We illustrate our information-geometric criterion for stability by an autocatalytic reaction model, where dynamics are driven by a nonlinear master equation.

Geometric Approach to Multiple-Time-Scale Kinetics: A Nonlinear Master Equation Describing Vibration-to-Vibration Relaxation

2001 ◽  
Vol 215 (2) ◽  
Author(s):  
M.J. Davis ◽  
R.T. Skodje
Keyword(s):  
Master Equation ◽  
Time Scale ◽  
Geometric Approach ◽  
Negative Eigenvalue ◽  
Multiple Time ◽  
Time Behavior ◽  
Multiple Time Scale ◽  
Approach To Equilibrium ◽  
Nonlinear Master Equation ◽  
Low Dimensional

A geometric approach to the study of multiple-time-scale kinetics is taken here. The approach to equilibrium for kinetic systems is studied via low-dimensional manifolds, with an application to a nonlinear master equation for vibrational relaxation. One of our main concerns is the asymptotic (in time) behavior of the system and whether there is a well-defined rate of approach to equilibrium. One-dimensional slow manifolds provide a good means for studying such behavior in nonlinear systems, because they are the analogue of the eigenvector with least negative eigenvalue for linear kinetics.

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