Tsallis q-Stat and the Evidence of Long-Range Interactions in Soil Temperature Dynamics.

Babalola O Ogunsua,John A Laoye

doi:10.3390/e23070909

Abstract

The complexities in the variations of soil temperature and thermal diffusion poses a physical problem that requires more understanding. The quest for a better understanding of the complexities of soil temperature variation has prompted the study of the q-statistics in the soil temperature variation with the view of understanding the underlying dynamics of the temperature variation and thermal diffusivity of the soil. In this work, the values of Tsallis stationary state q index known as q-stat were computed from soil temperature measured at different stations in Nigeria. The intrinsic variations of the soil temperature were derived from the soil temperature time series by detrending method to extract the influences of other types of variations from the atmosphere. The detrended soil temperature data sets were further analysed to fit the q-Gaussian model. Our results show that our datasets fit into the Tsallis Gaussian distributions with lower values of q-stat during rainy season and around the wet soil regions of Nigeria and the values of q-stat obtained for monthly data sets were mostly in the range for all stations, with very few values q closer to 1.2 for a few stations in the wet season. The distributions obtained from the detrended soil temperature data were mostly found to belong to the class of asymmetric q-Gaussians. The ability of the soil temperature data sets to fit into q-Gaussians might be due and the non-extensive statistical nature of the system and (or) consequently due to the presence of superstatistics. The possible mechanisms responsible this behaviour was further discussed.

Highlights

The complexities in soil thermal diffusion and the complex thermal interaction between the soil and the atmosphere could be responsible for the sporadic changes in the soil temperature measurements
The soil temperature time series was analysed to understand the statistical mechanics of the thermal diffusion processes and the energy transfer dynamics in the soil
In this work, the Tsallis non-extensive statistical mechanics was investigated in soil temperature dynamics to obtain the stationary q-index for soil temperature measured from different regions of Nigeria

Summary

Introduction

The complexities in soil thermal diffusion and the complex thermal interaction between the soil and the atmosphere could be responsible for the sporadic changes in the soil temperature measurements. Most atmospheric temperature systems are characterized by dynamical complexity This framework is based on the study of complexity in these systems considering the Tsallis statistical distribution. Relating the distributions describing natural systems such as the atmosphere to the presence of superstatistics could be a good reason for the possible presence of q-Gaussians. This because, like the ability to derive the superstatistics from q-Gaussians, the q-Gaussians can be derived from super statistics. We have investigated the complexity of soil temperature and thermal diffusivity dynamics for a better understanding of the statistical mechanics of its variation. Our ability to answer these questions will shed more light on soil temperature dynamics and provide a better understanding of the viability of the application of nonextensive statistical mechanics and Tsallis statistics to the characterization and modelling of soil temperature and soil thermal diffusivity in the future

Tsallis Statistical Formalism and q-Gaussians

Data and Methods

Results and Discussion

Conclusions