Partition function (statistical mechanics): Difference between revisions

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There are multiple approaches to deriving the partition function. The following derivation follows the more powerful and general [[information theory|information-theoretic]] [[Edwin Thompson Jaynes|Jaynesian]] [[maximum entropy thermodynamics|maximum entropy]] approach.

According to the [[second law of thermodynamics]], a system assumes a configuration of [[maximum entropy thermodynamics|maximum entropy]] at [[thermodynamic equilibrium]]{{Citation needed|reason=important statement with profound consequences|date=December 2016}}. We seek a probability distribution of states <math> \rho_i </math> that maximizes the discrete [[entropy (statistical thermodynamics)#Gibbs entropy formula|Gibbs entropy]]

<math display="block"> S = - k_\text{B} \sum_i \rho_i \ln \rho_i </math>