entropy can be expressed as a function of the state of the system.
entropy can be expressed as a function of the state of the system.
entropy can be expressed as a function of?
the state of the system
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
though the maximum entropy approach is based directly on informational entropy, it is applicable to physics only when there is a clear physical definition of entropy. there is no clear unique general physical definition of entropy for non-equilibrium systems, which are general physical systems considered during a process rather than thermodynamic systems in their own internal states of thermodynamic equilibrium. it follows that the maximum entropy approach will not be applicable to non-equilibrium systems until there is found a clear physical definition of entropy. this problem is related to the fact that heat may be transferred from a hotter to a colder physical system even when local thermodynamic equilibrium does not hold so that neither system has a well defined temperature. classical entropy is defined for a system in its own internal state of thermodynamic equilibrium, which is defined by state variables, with no non-zero fluxes, so that flux variables do not appear as state variables. but for a strongly non-equilibrium system, during a process, the state variables must include non-zero flux variables. classical physical definitions of entropy do not cover this case, especially when the fluxes are large enough to destroy local thermodynamic equilibrium. in other words, for entropy for non-equilibrium systems in general, the definition will need at least to involve specification of the process including non-zero fluxes, beyond the classical static thermodynamic state variables. the 'entropy' that is maximized needs to be defined suitably for the problem at hand. if an inappropriate 'entropy' is maximized, a wrong result is likely. in principle, maximum entropy thermodynamics does not refer narrowly and only to classical thermodynamic entropy. it is about informational entropy applied to physics, explicitly depending on the data used to formulate the problem at hand. according to attard, for physical problems analyzed by strongly non-equilibrium thermodynamics, several physically distinct kinds of entropy need to be considered, including what he calls second entropy. attard writes: "maximizing the second entropy over the microstates in the given initial macrostate gives the most likely target macrostate.". the physically defined second entropy can also be considered from an informational viewpoint.
maximum entropy thermodynamics