Vasil Avramov

We study information-theoretic and complexity measures for the Dunkl-supersymmetric harmonic oscillator to identify the effect of supersymmetry on these quantities. Using the Rakhmanov probability density of the Dunkl-SUSY functions, we analyze the Shannon entropy, spreading measures (Heller, Rényi, and Fisher lengths), and several statistical and dynamical complexities. The Shannon entropy is obtained both asymptotically and in closed analytic form, showing that supersymmetry does not affect the leading large-n scaling. In contrast, spreading measures reveal enhanced localization of the SUSY eigenstates relative to the standard harmonic oscillator. Finally, we find that LMC and Fisher–Shannon complexities are higher in the supersymmetric case.

We explore the sector of point-like string in Schrödinger spaces, reveal underlying supersymmetry and compute its Krylov complexity.

We suggest a finite-time geometric optimization framework to analyze thermal fluctuations and optimal processes in black holes. Our approach implement geodesics in thermodynamic space to define optimal pathways between equilibrium and non-equilibrium states. Since thermodynamic metrics need not be positive-definite, the method ensures a positive thermodynamic length by incorporating simple scale factor into the metric. We show that the thermodynamic length and the scale factor are sensitive to phase transitions in entropy representation, addressing a key gap in Hessian thermodynamic geometry. Additionally, we link the scale factor to the sign of thermodynamic curvature, connecting it to the information geometry governing optimal processes. Our results indicate that optimal fluctuations can drive the evaporation of Schwarzschild and Kerr black holes, which may significantly differ from Hawking radiation. We also explore optimal accretion-driven processes supported by an external inflow of energy.

This study is aimed at providing a thorough analysis of the classical thermodynamic stability of black holes within the Anti-de Sitter (AdS) family. We utilize the Nambu bracket formalism to calculate local heat capacities and employ Sylvester's criterion in the mass-energy ensemble to determine both local and global thermodynamic stability regions. Emphasizing the crucial role of the cosmological constant, we establish the conditions necessary for the existence of thermodynamically stable black hole configurations. Our work highlights the applicability of classical thermodynamics in understanding black hole physics, while acknowledging the potential deviations that may impact the observables of the system beyond the classical level.