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Ergodicity of non-Hamiltonian Equilibrium Systems

Evans D. J., Williams S. R., Rondoni L., Searles D. J.

Computational Methods in Science and Technology

2017

Vol. 23, No. 3

175--184

It is well known that ergodic theory can be used to formally prove a form of relaxation to microcanonical equilibrium for finite, mixing Hamiltonian systems. In this manuscript we substantially modify this proof using an approach similar to that used in umbrella sampling, and use this approach to consider relaxation in both Hamiltonian and non- Hamiltonian systems. In doing so, we demonstrate the need for a form of ergodic consistency of the initial and final distribution. The approach only applies to relaxation of averages of physical properties and low order probability distribution functions. It does not provide any information about whether the full 6N-dimensional phase space distribution relaxes towards the equilibrium distribution or how long the relaxation of physical averages takes.

Ergodic theory approach to chaos: remarks and computational aspects

Mitkowski P. J., Mitkowski W.

International Journal of Applied Mathematics and Computer Science

2012

Vol. 22, no. 2

259-267

We discuss basic notions of the ergodic theory approach to chaos. Based on simple examples we show some characteristic features of ergodic and mixing behaviour. Then we investigate an infinite dimensional model (delay differential equation) of erythropoiesis (red blood cell production process) formulated by Lasota. We show its computational analysis on the previously presented theory and examples. Our calculations suggest that the infinite dimensional model considered possesses an attractor of a nonsimple structure, supporting an invariant mixing measure. This observation verifies Lasota's conjecture concerning nontrivial ergodic properties of the model.

Finite sequences of subshits of finite type

Jabłoński D.

Demonstratio Mathematica

2005

Vol. 38, nr 4

965-975

The goal of this paper is to present some dynamical properties of finite sequences of finite type subshifts. Moreover, some conditions for algorithmization of these properties are formulated.