An Emergence View Of Statistical Mechanics And Classical Physics
From Darwinian Dynamics
Ping Ao, Mechanical Engineering, University of Washington
We present here an exploration on the physics implications of the
Darwinian dynamics from biological sciences. We first show how the
nonequilibrium statistical mechanics emerges naturally: the
Darwinian dynamics emphasizes the role of the canonical ensemble,
hence the Boltzmann-Gibbs type distribution function. We then show
that the first three laws of the thermodynamics, the Zeroth Law,
the First Law and the Second Law can be followed from the
Darwinian dynamics, except the Third Law. The inability to derive
the Third Law indicates that the Darwinian dynamics belongs to the
"classical" domain. Specifically, the Second Law is proved from
the dynamical point of view. Two types of current dynamical
equalities are explicitly discussed in the present framework: one
is based on Feynman-Kac formula and one is a generalization of the
Einstein relation. Both are directly accessible to experimental
tests. Our demonstration indicates that the Darwinian dynamics is
logically a simple and straightforward starting point to get into
thermodynamics and is complementary to the conservative dynamics
dominated in physical sciences.
Online Manuscript: P. Ao, physics/0512252