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Summary

At the microscale, the motion of atoms and molecules composing matter is governed by Hamiltonian dynamics. For classical systems, this motion is described as trajectories in the phase space of the positions and momenta of the particles. Different equilibrium and nonequilibrium statistical ensembles can be introduced, each associated with some probability distribution, which is a solution of Liouville’s equation. The BBGKY hierarchy of equations is obtained for the multiparticle distribution functions. The presentation includes the properties of ergodicity and dynamical mixing, the Pollicott–Ruelle resonances, microreversibility, and the nonequilibrium breaking of time-reversal symmetry at the statistical level of description. The concept of entropy is introduced by coarse graining. Linear response theory is developed within the classical framework, leading to the Onsager–Casimir reciprocal relations and the fluctuation–dissipation theorem. The projection-operator methods are summarized.

It is shown that methods used by the author to approximate limit probabilities for Markov processes from their Q-matrices extend to semi-Markov processes. The limit probabilities for semi-Markov processes can be approximated using only truncations of the embedded Markov chain transition matrix and the vector of mean holding times.

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2 - Statistical Mechanics

Summary

Truncation approximation of the limit probabilities for denumerable semi-Markov processes

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2 results

2 - Statistical Mechanics

Summary

Truncation approximation of the limit probabilities for denumerable semi-Markov processes