Active matter models are composed of many elements that interact among them. Each element has a few degrees of freedom (position and orientation) and operates with a simple dissipative dynamic. Its interactions are also very simples; for example, bacteria consider the excluded volume and the alignment of pairs. Thus, they are a prototypical example of a non-equilibrium system, where the non-equilibrium character is at a microscopic scale. Since is a compound of many elements, it becomes obvious to use the statistic mechanics tools to describe the emergent and collective properties of these systems.
During the first three years of this Nucleus, the focus of the study was the generic fluctuant processes of the activity, besides the feedback among different components and the biological activity information flows.

The investigation work included the durotaxis, phoretic forces, and self-assembly. In this new stage (2021-2023), the Millennial Nucleus seeks to enhance the description of the active matter at collective scales, starting with motion equations of the constituents. For this, we will use theoretical approaches like kinetics theory, hydrodynamic descriptions, and fluctuant hydrodynamics. Simultaneously, we will be doing intensive numeric simulations of simple models of the studied systems at a large scale.
One of the most characteristic phenomena of the thermodynamic systems is the phase transitions and the shown active matter. In the next three years, we will be studying the universality and dynamics of transitions in wetting and clustering phases.