Established expressions for entropy production in irreversible processes are generalized to include friction explicitly, as a source of irreversibility in the interaction between a system and its surroundings. The net amount of heat delivered to the system does not come now only from the reservoir, but may have an additional component coming from the work done against friction forces and dissipated as heat. To avoid ambiguities in interpreting the different contributions to entropy increase, the latter is also written in terms of the heat directly exchanged between the system and surroundings and of the fraction of frictional work that is lost in the system.
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João P. S. Bizarro (2008) studied this question.
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