* Astronomy

Title: The Arrow of Time in the collapse of collisionless self-gravitating systems: non-validity of the Vlasov-Poisson equation during violent relaxation
Author: Leandro Beraldo e Silva, Walter de Siqueira Pedra, Laerte Sodré, Eder Perico, Marcos Lima

The collapse of a collisionless self-gravitating system, with the fast achievement of a quasi-stationary state, is driven by violent relaxation, with a typical particle interacting with the time-changing collective gravitational potential. It is traditionally assumed that this evolution is described by the (time-reversible) Vlasov-Poisson equation, in which case entropy must be conserved. We use N-body simulations to follow the evolution of an isolated self-gravitating system, estimating the (fine-grained) distribution function and the corresponding Shannon entropy. We do this with three different codes: NBODY-6 (direct summation without softening), NBODY-2 (direct summation with softening) and GADGET-2 (tree code with softening), for different numbers of particles and initial conditions. We find that during violent relaxation entropy increases in a way that cannot be described by 2-body relaxation as modeled by the Fokker-Planck approximation. On the other hand, the long-term evolution is very well described by this model. Our results imply that the violent relaxation process must be described by a kinetic equation other than the Vlasov-Poisson, even if the system is collisionless. Our estimators provide a general method for testing any proposed kinetic equation. We also study the dependence of the 2-body relaxation time-scale tau_{col} on the number of particles N, obtaining tau_{col}\propto \sqrt{N}, and the dependence of tau_{col} on the softening length \varepsilon, which can be fit by a function of the form tau_{col} \propto \sqrt{\varepsilon}\cdot e^{c\varepsilon}, for a fixed number of particles.

Read more (423kb, PDF)

Title: On the nature of cosmological time
Author: Pierre Magain, Clémentine Hauret

Time is a parameter playing a central role in our most fundamental modeling of natural laws. Relativity theory shows that the comparison of times measured by different clocks depends on their relative motions and on the strength of the gravitational field in which they are embedded. In standard cosmology, the time parameter is the one measured by fundamental clocks, i.e. clocks at rest with respect to the expanding space. This proper time is assumed to flow at a constant rate throughout the whole history of the Universe. We make the alternative hypothesis that the rate at which cosmological time flows depends on the dynamical state of the Universe. In thermodynamics, the arrow of time is strongly related to the second law, which states that the entropy of an isolated system will always increase with time or, at best, stay constant. Hence, we assume that time measured by fundamental clocks is proportional to the entropy of the region of the Universe that is causally connected to them. Under that simple assumption, we build a cosmological model that explains the Type Ia Supernovae data (the best cosmological standard candles) without the need for exotic dark matter nor dark energy.

Read more (57kb, PDF)

Title: On the time arrows, and randomness in cosmological signals
Authors: V.G.Gurzadyan, S.Sargsyan, G.Yegorian

Arrows of time - thermodynamical, cosmological, electromagnetic, quantum mechanical, psychological - are basic properties of Nature. For a quantum system-bath closed system the de-correlated initial conditions and no-memory (Markovian) dynamics are outlined as necessary conditions for the appearance of the thermodynamical arrow. The emergence of the arrow for the system evolving according to non-unitary dynamics due to the presence of the bath, then, is a result of limited observability, and we conjecture the arrow in the observable Universe as determined by the dark sector acting as a bath. The voids in the large scale matter distribution induce hyperbolicity of the null geodesics, with possible observational consequences.

Read more (609kb, PDF)

Time is slowing

Scientists say time is gradually slowing down and will eventually grind to a halt, freezing everything in an instant.
But the change is so subtle it is undetectable to human senses and would only become noticeable over billions of years, when the Earth is long gone.
The idea has been set out by Professor Jose Senovilla and colleagues Marc Mars and Raul Vera of the University of the Basque Country, Bilbao, and University of Salamanca, near Madrid.
Read more 

Time is running out - literally, says scientist

Dec 2007 Scientists have come up with the radical suggestion that the universe's end may come not with a bang but a standstill - that time could be literally running out and could, one day, stop altogether.
The idea that time itself could cease to be in billions of years - and everything will grind to a halt - has been set out by Professor José Senovilla, Marc Mars and Raül Vera of the University of the Basque Country, Bilbao, and University of Salamanca, Spain.
Read more