text: Electronic entropy is the entropy of a system attributable to electrons' probabilistic occupation of states. This entropy can take a number of forms. The first form can be termed a density of states based entropy. The Fermi–Dirac distribution implies that each eigenstate of a system, , is occupied with a certain probability, . As the entropy is given by a sum over the probabilities of occupation of those states, there is an entropy associated with the occupation of the various electronic states. In most molecular systems, the energy spacing between the highest occupied molecular orbital and the lowest unoccupied molecular orbital is usually large, and thus the probabilities associated with the occupation of the excited states are small. Therefore, the electronic entropy in molecular systems can safely be neglected. Electronic entropy is thus most relevant for the thermodynamics of condensed phases, where the density of states at the Fermi level can be quite large, and the electronic entropy can thus contribute substantially to thermodynamic behavior. A second form of electronic entropy can be attributed to the configurational entropy associated with localized electrons and holes. This entropy is similar in form to the configurational entropy associated with the mixing of atoms on a lattice.
  Electronic entropy can substantially modify phase behavior, as in lithium ion battery electrodes, high temperature superconductors, and some perovskites. It is also the driving force for the coupling of heat and charge transport in thermoelectric materials, via the Onsager reciprocal relations.