# Probability, ergodicity, irreversibility and dynamical systems

@article{Lucia2008ProbabilityEI, title={Probability, ergodicity, irreversibility and dynamical systems}, author={Umberto Lucia}, journal={Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences}, year={2008}, volume={464}, pages={1089 - 1104} }

The problem of irreversibility is difficult and part of this difficulty is due to dealing with the statistical mechanics of a large number of particles. The ergodic theory, founded on the link between thermodynamics and its statistical probability, introduced the ergodic theorem that consists of the equality of microcanonical phase average and the time average of the observables. Moreover, a global approach has been introduced, starting from non-equilibrium thermodynamics and obtaining a…

## 70 Citations

Time, Irreversibility and Entropy Production in Nonequilibrium Systems

- PhysicsEntropy
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A focus is on the notion of entropy generation as the marked characteristic of irreversible behaviour in time and irreversibility, in order to link macroscopic to microscopic approaches to these complicated problems.

The thermodynamic hamiltonian for open systems

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- 2011

The variational method is very important in mathematical and theoretical physics because it allows us to describe the natural systems by physical quantities independently from the frame of reference…

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- Mathematics, Computer ScienceProceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences
- 2016

Dynamics equations which describe the behaviour of non-stationary processes that follow the maximum Rényi entropy principle are proposed and the uniqueness of the limit distribution and asymptotic convergence of the PDF for both cases is demonstrated.

Paths and stochastic order in open systems

- Mathematics
- 2011

The principle of maximum irreversible is proved to be a consequence of a stochastic order of the paths inside the phase space; indeed, the system evolves on the greatest path in the stochastic order.…

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