Minimal black holes and species thermodynamics explore the connection between species and black holes in gravitational effective theories. The species scale, defined as $ \Lambda_{sp} = \frac{M_{P}}{N_{sp}^{\frac{1}{d-2}}} $, sets a lower bound on the shortest possible length that can be probed. Species thermodynamics, akin to black hole thermodynamics, describes species as having entropy, temperature, and mass that follow thermodynamic laws. For uncharged species, the species entropy $ \mathcal{S}_{sp} \simeq (L_{sp}M_{P})^{d-2} $, while the temperature $ T_{sp} \simeq \Lambda_{sp} $. For charged species, the temperature is $ T_{sp} \simeq \Lambda_{sp}^2 $, reflecting their different thermodynamic behavior.
The paper extends the thermodynamic interpretation of species to charged cases, examining modifications in thermodynamic properties of near-extremal charged species. It explores implications for cosmology, particularly in the Dark Dimension scenario, where species decay rates align with properties of KK dark matter particles. The study also investigates microscopic constructions in non-supersymmetric string theories, where towers of charged near-extremal species may arise. The analysis includes the duality between species particles and black hole geometries, and the role of species in cosmology, suggesting their potential as dark matter candidates. The thermodynamic relations for charged species are consistent with those for black holes, with the species temperature being suppressed by a factor of $ S_{sp}^{-\frac{1}{d-2}} $ compared to uncharged species. The quantum decay rate of species is found to depend on entropy suppression, with the decay rate being reduced for large entropy. The paper concludes that species thermodynamics provides a framework for understanding the behavior of species in gravitational effective theories, with implications for cosmology and dark matter.Minimal black holes and species thermodynamics explore the connection between species and black holes in gravitational effective theories. The species scale, defined as $ \Lambda_{sp} = \frac{M_{P}}{N_{sp}^{\frac{1}{d-2}}} $, sets a lower bound on the shortest possible length that can be probed. Species thermodynamics, akin to black hole thermodynamics, describes species as having entropy, temperature, and mass that follow thermodynamic laws. For uncharged species, the species entropy $ \mathcal{S}_{sp} \simeq (L_{sp}M_{P})^{d-2} $, while the temperature $ T_{sp} \simeq \Lambda_{sp} $. For charged species, the temperature is $ T_{sp} \simeq \Lambda_{sp}^2 $, reflecting their different thermodynamic behavior.
The paper extends the thermodynamic interpretation of species to charged cases, examining modifications in thermodynamic properties of near-extremal charged species. It explores implications for cosmology, particularly in the Dark Dimension scenario, where species decay rates align with properties of KK dark matter particles. The study also investigates microscopic constructions in non-supersymmetric string theories, where towers of charged near-extremal species may arise. The analysis includes the duality between species particles and black hole geometries, and the role of species in cosmology, suggesting their potential as dark matter candidates. The thermodynamic relations for charged species are consistent with those for black holes, with the species temperature being suppressed by a factor of $ S_{sp}^{-\frac{1}{d-2}} $ compared to uncharged species. The quantum decay rate of species is found to depend on entropy suppression, with the decay rate being reduced for large entropy. The paper concludes that species thermodynamics provides a framework for understanding the behavior of species in gravitational effective theories, with implications for cosmology and dark matter.