Thermodynamic approach to network dismantling under uncertainty

This thesis investigates the dismantling of complex networks under partial topological knowledge, a scenario that challenges the common assumption of complete information. The research first evaluates the limitations of standard centrality-based attacks when only limited sampling is available. It then explores the possibility of defining new exploration criteria based on partition function minimization; however, results show that these approaches collapse into a much simpler, moderately effective heuristic. Consequently, the focus shifts to the development of an analytical protocol that extends the Cavity Method to the Laplacian matrix. This method allows for the determination of the density matrix spectrum during a non-Markovian random walk attack, theoretically validating empirical observations without requiring numerical diagonalization. The framework provides a robust tool to quantify the entropy and free energy of the system as it disintegrates.