HI Arif --
I think this idea is not so new -- and may well recall the
"dissipative structures" model of I. Prigogine.
In one sense, it need not say very much --
since, if we use Botlzmann's idea of entropy as probability,
then it can just say that what actually happens is the most probable thing that can happen.
However, Botzmann used his argument in the context of equilibrium arrangements
of molecules, and a key question is what happens if we relax that condition
and ask about non-equilibrium configurations.
Non-equilibrium arrangements are found in nature, in the populations
of energy levels of atoms, for example, when there is a "pumping mechanism"
that can drive the population of a particular line into a non-equilibrium
arrangement, often involving the population of some other nearby line.
In our paper, we looked at Boltzmann's equation
Entropy = k log (Probability of arrangement)
and imagined this arrangement slowly driven into non-equilibrium
by a factor gamma = 1+ epsilon, where epsilon is a small quantity.
If epsilon is zero then gamma = 1
and the small change of entropy = log (gamma) is zero.
For a dissipative process, we expect a decline in the population
of energized states, and so epsilon would be negative,
and so would log gamma. However, we would associate this
change -- normally -- with a non-driven relaxation, and so increased entropy.
We therefore put a minus sign in front of the term k log(gamma).
For a driven process, we would find an increasingly improbable
distribution of higher energy states (as seen from the point of view
of the external universe as a whole). Thus as the biosphere
steadily grows -- by the factor epsilon each year -- the entropy
of that biosphere would become slowly smaller.
It would be less likely to be found by pure chance in a non-driven
arrangements of molecules. We described this as a growth
of negative entropy.
There is a sign convention in this which is perhaps a matter of choice.
And, in an open system, a decline in entropy of one component
associates with a corresponding increase in another part of the open system.
So I think all this can be put together so as to make a feasible
physical picture. However, it is far from complete like this.
It does not say what the driving mechanism actually is,
nor does it relate it to particular molecules that are found in the
driving locations of observed cells.
However, it may be useful to apply to more generalized concepts
and environments where life forms might exist of a completely unknown type.
Best wishes,
Ed