 
Summary: The second entropy: a general theory for
nonequilibrium 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 nonequilibrium thermodynamics of timedependent
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 nonequilibrium systems. In contrast, the second law of
thermodynamics only provides a direction for change, not a rate of change.
The probability distribution function for timedependent systems is also
given, which is the focal point of nonequilibrium statistical mechanics. This
and the second entropy are used, for example, to derive the Langevin
equation, the GreenKubo relations, the transition and path probability,
the fluctuation and work theorems, and a generalised fluctuationdissipation
theorem. They are also used to develop computer simulation algorithms
