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}
}
  • U. Lucia
  • Published 8 May 2008
  • Physics
  • Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences
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… 
Time, Irreversibility and Entropy Production in Nonequilibrium Systems
TLDR
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
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
Dynamics of non-stationary processes that follow the maximum of the Rényi entropy principle
TLDR
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
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.
...
1
2
3
4
5
...

References

SHOWING 1-10 OF 26 REFERENCES
From virtual work principle to maximum entropy for nonequilibrium system
TLDR
This work is on the maximum of the entropy defined as a measure of the momentary dynamical uncertainty as a function of the probability distribution over the microstates of the system at any given moment.
Entropy production and thermodynamics of nonequilibrium stationary states: a point of view.
TLDR
The text first reviews the philosophy behind a recently proposed definition of entropy production in nonequilibrium stationary systems, and a detailed technical attempt at defining the entropy of a stationary states via their variational properties.
Information theory explanation of the fluctuation theorem, maximum entropy production and self-organized criticality in non-equilibrium stationary states
Jaynes' information theory formalism of statistical mechanics is applied to the stationary states of open, non-equilibrium systems. First, it is shown that the probability distribution pΓ of the
Second Law of Thermodynamics for Macroscopic Mechanics Coupled to Thermodynamic Degrees of Freedom
Starting from and only using classical Hamiltonian dynamics, we prove the maximum work principle in a system where macroscopic dynamical degrees of freedom are intrinsically coupled to microscopic
Nonequilibrium stationary states and entropy.
TLDR
It is conjecture that in a nonequilibrium stationary state the entropy is just a quantity that can be transferred or created, but has no physical meaning as "entropy content" as a property of the system.
Dynamical Ensembles in Nonequilibrium Statistical Mechanics.
TLDR
This presents the first test of the Ruelle principle on a many particle system far from equilibrium, and a specific prediction, obtained without the need to construct explicitly the SRB itself, is shown to be in agreement with a recent computer experiment on a strongly sheared fluid.
...
1
2
3
...