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Despite its simplicity, it seems to my best of knowledge that the possiblysimplest approach towards deriving equations governing irreversiblethermodynamics from gas-kinetic considerations within the framework ofclassical mechanics has never been pursued. In this paper we address thisomission and derive the equations describing the irreversible thermodynamics ofa gas in a piston and associated thermodynamic cycles performed in finite time.What we find is a thermodynamic action principle: The irreversible work werequire for performing a thermodynamic cycle in finite time times the time werequire to run through the cycle, a isothermal compression/decompression cyclefor instance, will always be larger or equal to a lower bound given by a systemspecific constant with the dimension of an action. This process specific actionconstants can take values of the order of Plank's constant for microscopicprocesses, such as displacing a Hydrogen atom by one atom diameter. Formacroscopic processes (e.g. a bicycle pump) also the action constant takesmacroscopically observable values. We discuss the finite time Carnot cycle, andestimate the lower bound for irreversible work required when rewritingphysically embodied bits of information and compare the resulting values withLandauer's bond, the irreversible amount of energy that needs to be dissipatedfor re-writing a bit.

An action principle of classical irreversible thermodynamics - Irreversible thermodynamic cycles and embodied bits of information