Efficiencies of thermodynamics when temperature-dependent energy levels exist

What is it about?

In contemporary statistical mechanics, the effect of energy levels that depend on temperature does not appear explicitly in the formalism. But in 1940's and later, prominent physicists have seriously argued incorporation of this effect into the framework. It entails heat but they did not consider impact on thermodynamics efficiencies at that time. This article explores such challenges.

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Why is it important?

Now there are many theoretical works and experiments that exhibits temperature dependent energy levels in the study of semiconductors. Especially thermoelectric effects are important platform to harvesting electricity in industrial levels. Theoretical considerations would be of help or needed to evaluate accurate performances of various types of thermoelectric materials.