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

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

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