19,214 research outputs found
Cycle symmetry, limit theorems, and fluctuation theorems for diffusion processes on the circle
Cyclic structure and dynamics are of great interest in both the fields of
stochastic processes and nonequilibrium statistical physics. In this paper, we
find a new symmetry of the Brownian motion named as the quasi-time-reversal
invariance. It turns out that such an invariance of the Brownian motion is the
key to prove the cycle symmetry for diffusion processes on the circle, which
says that the distributions of the forming times of the forward and backward
cycles, given that the corresponding cycle is formed earlier than the other,
are exactly the same. With the aid of the cycle symmetry, we prove the strong
law of large numbers, functional central limit theorem, and large deviation
principle for the sample circulations and net circulations of diffusion
processes on the circle. The cycle symmetry is further applied to obtain
various types of fluctuation theorems for the sample circulations, net
circulation, and entropy production rate.Comment: 28 page
Constraints on the Brans-Dicke gravity theory with the Planck data
Based on the new cosmic CMB temperature data from the Planck satellite, the 9
year polarization data from the WMAP, the BAO distance ratio data from the SDSS
and 6dF surveys, we place a new constraint on the Brans-Dicke theory. We adopt
a parametrization \zeta=\ln(1+1/\omega}), where the general relativity (GR)
limit corresponds to . We find no evidence of deviation from general
relativity. At 95% probability, , correspondingly,
the region is excluded. If we restrict ourselves to
the (i.e. ) case, then the 95% probability interval is
. We can also translate this
result to a constraint on the variation of gravitational constant, and find the
variation rate today as yr ( error bar), the integrated change since the epoch of
recombination is ( error
bar). These limits on the variation of gravitational constant are comparable
with the precision of solar system experiments.Comment: 7 pages, 5 figures, 2 table
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