  Despite its simplicity, it seems to my best of knowledge that the possibly
simplest approach towards deriving equations governing irreversible
thermodynamics from gas-kinetic considerations within the framework of
classical mechanics has never been pursued. In this paper we address this
omission and derive the equations describing the irreversible thermodynamics of
a gas in a piston and associated thermodynamic cycles performed in finite time.
What we find is a thermodynamic action principle: The irreversible work we
require for performing a thermodynamic cycle in finite time times the time we
require to run through the cycle, a isothermal compression/decompression cycle
for instance, will always be larger or equal to a lower bound given by a system
specific constant with the dimension of an action. This process specific action
constants can take values of the order of Plank's constant for microscopic
processes, such as displacing a Hydrogen atom by one atom diameter. For
macroscopic processes (e.g. a bicycle pump) also the action constant takes
macroscopically observable values. We discuss the finite time Carnot cycle, and
estimate the lower bound for irreversible work required when rewriting
physically embodied bits of information and compare the resulting values with
Landauer's bond, the irreversible amount of energy that needs to be dissipated
for re-writing a bit.
