Symmetry and symmetry-breaking in soil pores and climate change mitigation: What fractal geometry can tell us?

Soil is a critical component of terrestrial ecosystems, directly influencing global biogeochemical cycles. Despite its importance, the complex architecture of soil pores and their impact on greenhouse gas emissions remain poorly understood. This perspective aims to address this gap by applying symmetry and symmetry-breaking concepts through fractal geometry to elucidate the structural and functional complexities of soil pores. We highlight how fractal parameters can quantify the self-similar nature of soil pore structures, revealing their size, shape, and connectivity. These geometric attributes influence soil properties such as permeability and diffusivity, which are essential for understanding gas exchange and microbial activity within the soil matrix. Furthermore, we emphasize the effects of various land management practices, including tillage and wetting-drying cycles, on soil pore complexity using three-dimensional multi-fractal analysis. Literature indicates that different agricultural practices significantly alter pore heterogeneity and connectivity, affecting greenhouse gas emissions. Conventional tillage decreases pore connectivity and increases randomness, whereas no-tillage preserves larger, more complex pore structures. We propose that integrating combinatorial, geometric, and functional symmetry concepts offers a comprehensive framework for examining the structure-property-function relationships in soil. This novel approach could enhance our understanding of soil's role in the global cycle of greenhouse gases and provide insights into sustainable land management practices aimed at mitigating climate change.