170,215 research outputs found
Gibbs entropy and irreversible thermodynamics
Recently a number of approaches has been developed to connect the microscopic
dynamics of particle systems to the macroscopic properties of systems in
nonequilibrium stationary states, via the theory of dynamical systems. This way
a direct connection between dynamics and Irreversible Thermodynamics has been
claimed to have been found. However, the main quantity used in these studies is
a (coarse-grained) Gibbs entropy, which to us does not seem suitable, in its
present form, to characterize nonequilibrium states. Various simplified models
have also been devised to give explicit examples of how the coarse-grained
approach may succeed in giving a full description of the Irreversible
Thermodynamics. We analyze some of these models pointing out a number of
difficulties which, in our opinion, need to be overcome in order to establish a
physically relevant connection between these models and Irreversible
Thermodynamics.Comment: 19 pages, 4 eps figures, LaTeX2
The Evolution of Substructure in Galaxy, Group and Cluster Haloes I: Basic Dynamics
The hierarchical mergers that form the haloes of dark matter surrounding
galaxies, groups and clusters are not entirely efficient, leaving substantial
amounts of dense substructure, in the form of stripped halo cores or
`subhaloes', orbiting within these systems. Using a semi-analytic model of
satellite dynamics, we study the evolution of haloes as they merge
hierarchically, to determine how much substructure survives merging and how the
properties of individual subhaloes change over time. We find that subhaloes
evolve, due to mass loss, orbital decay, and tidal disruption, on a
characteristic time-scale equal to the period of radial oscillations at the
virial radius of the system. Subhaloes with realistic densities and density
profiles lose 25-45 per cent of their mass per pericentric passage, depending
on their concentration and on the circularity of their orbit. As the halo
grows, the subhalo orbits also grow in size and become less bound. Based on
these general patterns, we suggest a method for including realistic amounts of
substructure in semi-analytic models based on merger trees. We show that the
parameters in the resulting model can be fixed by requiring self-consistency
between different levels of the merger hierarchy. In a companion paper, we will
compare the results of our model with numerical simulations of halo formation.Comment: 20 pages, 20 figures; submitted to MNRA
Markov Chains and Dynamical Systems: The Open System Point of View
This article presents several results establishing connections be- tween
Markov chains and dynamical systems, from the point of view of open systems in
physics. We show how all Markov chains can be understood as the information on
one component that we get from a dynamical system on a product system, when
losing information on the other component. We show that passing from the
deterministic dynamics to the random one is character- ized by the loss of
algebra morphism property; it is also characterized by the loss of
reversibility. In the continuous time framework, we show that the solu- tions
of stochastic dierential equations are actually deterministic dynamical systems
on a particular product space. When losing the information on one component, we
recover the usual associated Markov semigroup
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