## 1. Introduction

[2] The Probability Distribution Function (PDF) of field differences provide a direct approach to describe the statistical properties of magnetic field fluctuations in solar wind. The traditional analyses were based on Boltzmann-Gibbs statistical mechanics which cannot describe physical systems which are not in thermal equilibrium. Though many studies have clearly presented the non-Gaussian feature of distributions of magnetic difference on relatively minor scales [*Marsch and Tu*, 1994, 1997], a quantitative way to characterize the fluctuations is still required. By introducing the nonextensive entropy *S*_{q} = *k*∑(1 − *p*_{i}^{q})/(*q* − 1) (with *q* ∈ *R*, and *S*_{1} = *S*_{BG}), *Tsallis* [1988] extended the B-G statistical mechanics, where *p*_{i} is the probability of the microstate, and q is a scale-dependent constant measuring the nonextensivity. To obtain the thermal equilibrium distribution, *S*_{q} is optimized with two energy constraint, and the Tsallis q-distribution function is defined as:

where x is physical quantity such as magnetic magnitude; *A*, *B*, and *q* are scale dependent parameters [*Tsallis and Brigatti*, 2004]. In the limit *q* → 1, the statistical mechanics of Tsallis recovers to the usual Boltzmann-Gibbs mechanics, and Gaussian distribution is recovered as a limiting case [*Tsallis et al.*, 2004]. The Tsallis distribution has been applied to describe many physical system in which long-range forces or long-term memory effects are dominated, such as fluxes of cosmic ray [*Tsallis et al.*, 2003], turbulence [*Beck*, 2001], and solar wind.

[3] *Burlaga and Viñas* [2004] first used Tsallis statistical mechanics to analyze the magnetic strength differences. They found that the PDF of magnetic strength increment at 1 AU on scales from 1 hour to 171 days can be described by Tsallis distribution. They also used Tsallis distribution to described fluctuations in daily observations of B between 7 and 87 AU on scales from 1 to 128 days [*Burlaga and Viñas*, 2005]. *Burlaga et al.* [2006] observed the Tsallis distribution of magnetic strength differences in the heliosheath. In the recent works, *Burlaga et al.* [2007] and *Burlaga and Viñas* [2007] stated that The PDFs of the increments of B are Tsallis distributions on scales from 1 hr-128 days between 1 and 90 AU and they applied a deterministic MHD model to predict these results. The predictions of the model agree with the observations from Voyager 1 at 80 AU. Thus, It has been proved that the fluctuations of B from 1 AU to heliosheath can be described by Tsallis distribution on a very wide range of scales.

[4] Venus Express was launched on 9 November 2005, and placed in elliptical orbits about the Venus [*Titov et al.*, 2006]. Despite of aiming at exploring the Venusian atmosphere, it spends majority of it 24-hour period in solar wind, thus it provides good opportunity to research the interplanetary magnetic field at 0.72 AU, and to extend the new statistical conclusion to inner heliosphere.