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Summary: The second entropy: a general theory for
non-equilibrium thermodynamics and
statistical mechanics
Phil Attard
DOI: 10.1039/b802697c
The second entropy is introduced, which is a new type of entropy that
provides a basis for the non-equilibrium thermodynamics of time-dependent
systems. Whereas the first or ordinary entropy counts the molecular
configurations associated with a given structure, the second entropy counts
the molecular configurations associated with a transition between two given
structures in a specified time. Maximization of the second entropy gives the
optimum rate of change or flux, and as such it provides a quantitative
principle for non-equilibrium systems. In contrast, the second law of
thermodynamics only provides a direction for change, not a rate of change.
The probability distribution function for time-dependent systems is also
given, which is the focal point of non-equilibrium statistical mechanics. This
and the second entropy are used, for example, to derive the Langevin
equation, the Green-Kubo relations, the transition and path probability,
the fluctuation and work theorems, and a generalised fluctuation-dissipation
theorem. They are also used to develop computer simulation algorithms
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