Understanding the process of earthquake preparation is of utmost importance in mitigating the potential damage caused by seismic events. That is why the study of seismic precursors is fundamental. However, the community studying non-seismic precursors relies on measurements, methods, and theories that lack a causal relationship with the earthquakes they claim to predict, generating skepticism among classical seismologists. Nonetheless, in recent years, a group has emerged that seeks to bridge the gap between these communities by applying fundamental laws of physics, such as the application of the second law of thermodynamics in multiscale systems. These systems, characterized by describing irreversible processes, are described by a global parameter called thermodynamic fractal dimension, denoted as (Formula presented.). A decrease in (Formula presented.) indicates that the system starts seeking to release excess energy on a macroscopic scale, increasing entropy. It has been found that the decrease in (Formula presented.) prior to major earthquakes is related to the increase in the size of microcracks and the emission of electromagnetic signals in localized zones, as well as the decrease in the ratio of large to small earthquakes known as the b-value. However, it is still necessary to elucidate how (Formula presented.), which is also associated with the roughness of surfaces, relates to other rupture parameters such as residual energy, magnitude, or fracture energy. Hence, this work establishes analytical relationships among them. Particularly, it is found that larger magnitude earthquakes with higher residual energy are associated with smoother faults. This indicates that the pre-seismic processes, which give rise to both seismic and non-seismic precursor signals, must also be accompanied by changes in the geometric properties of faults. Therefore, it can be concluded that all types of precursors (seismic or non-seismic), changes in fault smoothness, and the occurrence of earthquakes are different manifestations of the same multiscale dissipative system. © 2023 by the authors.