However, Boltzmann-Gibbs statistical mechanics has limitations. For example, its predictions can fail when a system is in certain regimes, such as phase transitions or critical phenomena. For instance ...

Statistical Learning Theory provides a mathematical framework for understanding how algorithms infer predictive rules from data. At its core lies the notion of risk: the expected loss of a model on ...

Statistical mechanics is one of the pillars of modern physics. Ludwig Boltzmann (1844-1906) and Josiah Willard Gibbs (1839-1903) were its primary formulators. They both worked to establish a bridge ...

For instance, statistical mechanics predicts the divergence of certain thermodynamic quantities at critical points, which is not observed experimentally. This has led to the development of the ...