Abiogenesis and the Second Law of Thermodynamics
399
rigged Hilbert space formulation of resonances. Nevertheless, some reviewers of the
work by the Brussels-Austin Group [31, 32] assert that the local origin of irreversibility has yet to be unambiguously proven, which might seem to be reasonable in view
of the philosophical evaluations discussed earlier. However, Bricmont
12 [32], see
also [33–35], goes one step further stating that Boltzmann’s late-nineteen-century
formulation is fully satisfactory
13 and that Prigogine does not pay sufficient attention
to the fundamental attributes of the classical explanation of irreversibility, i.e. to the
initial conditions and to the distinction between microscopic and macroscopic variables. He also states [32]: Although the quantum picture may be more complicated, I
do not believe that it renders obsolete the basic ideas explained here. It is evident that
the presently offered viewpoints will confront these statements. The quantum picture
is not only fundamental but it will by necessity add more options and possibilities as
will be demonstrated below.
The general conclusion so far is that the Brussels-Austin School should be essentially correct in that their mathematical formulation does not incorporate any approximations that exposes their sub-dynamical evolution with any unveiled epistemic
attributes. However, their work
14 is not entirely able to resolve questions such as:
why does nature choose one privileged direction of time, how does time symmetric
physics lead to time-asymmetric chemistry, conservative reversible dynamics result
in dissipative irreversible evolution and unitary time evolution convert to a contractive semigroup? These topics were already discussed at length during the Uppsala
Nobel Jubilee Meeting, Frontiers of Science, in 1991 [36], and in particular at the
associated Satellite Nobel Symposium, Resonances and Microscopic Irreversibility [30]. Although full agreement between the various groups could not be attained
some tentative lines of thought were documented [30]: (i) there exist intrinsically
irreversible systems with the chosen time direction compatible with the cosmological
arrow of time, (ii) there exists some kind of informity rule, i.e. a certain unavoidable
natural loss of information, which is compatible with broken temporal symmetry.
One should be reminded that the key problem related to abiogenesis, i.e. the biological machinery behind evolution or rather to find an understanding of the coupling
mechanism behind the selection of a functional macro-molecular structure from a big
molecular library, has yet to be resolved. An answer will be given in the following
sections, coming as an additional bonus of the quantum theoretical mathematical
formulation. In more detail we will derive, for each CES, the boundary condition
that links the micro- and the macroscopic levels finding the relation between the
temperature, the time scales and the dimension of the active degrees of freedom.
12 Bricmont refers to Lanford’s original derivation of Boltzmann’s equation [33].
13 Lanford’s theorem in the case of N hard spheres was extended in [34]. The review [35] nevertheless concludes: Boltzmann’s 1872 effort, to conciliate microscopic time-reversible dynamics with
increase of entropy and trend to equilibrium, still remains as a source of challenging mathematical
problems.
14 It is hard to evaluate general statements made here, since the fundamental difference between CM
and QM at the end of the day turns out to be significant.
399
rigged Hilbert space formulation of resonances. Nevertheless, some reviewers of the
work by the Brussels-Austin Group [31, 32] assert that the local origin of irreversibility has yet to be unambiguously proven, which might seem to be reasonable in view
of the philosophical evaluations discussed earlier. However, Bricmont
12 [32], see
also [33–35], goes one step further stating that Boltzmann’s late-nineteen-century
formulation is fully satisfactory
13 and that Prigogine does not pay sufficient attention
to the fundamental attributes of the classical explanation of irreversibility, i.e. to the
initial conditions and to the distinction between microscopic and macroscopic variables. He also states [32]: Although the quantum picture may be more complicated, I
do not believe that it renders obsolete the basic ideas explained here. It is evident that
the presently offered viewpoints will confront these statements. The quantum picture
is not only fundamental but it will by necessity add more options and possibilities as
will be demonstrated below.
The general conclusion so far is that the Brussels-Austin School should be essentially correct in that their mathematical formulation does not incorporate any approximations that exposes their sub-dynamical evolution with any unveiled epistemic
attributes. However, their work
14 is not entirely able to resolve questions such as:
why does nature choose one privileged direction of time, how does time symmetric
physics lead to time-asymmetric chemistry, conservative reversible dynamics result
in dissipative irreversible evolution and unitary time evolution convert to a contractive semigroup? These topics were already discussed at length during the Uppsala
Nobel Jubilee Meeting, Frontiers of Science, in 1991 [36], and in particular at the
associated Satellite Nobel Symposium, Resonances and Microscopic Irreversibility [30]. Although full agreement between the various groups could not be attained
some tentative lines of thought were documented [30]: (i) there exist intrinsically
irreversible systems with the chosen time direction compatible with the cosmological
arrow of time, (ii) there exists some kind of informity rule, i.e. a certain unavoidable
natural loss of information, which is compatible with broken temporal symmetry.
One should be reminded that the key problem related to abiogenesis, i.e. the biological machinery behind evolution or rather to find an understanding of the coupling
mechanism behind the selection of a functional macro-molecular structure from a big
molecular library, has yet to be resolved. An answer will be given in the following
sections, coming as an additional bonus of the quantum theoretical mathematical
formulation. In more detail we will derive, for each CES, the boundary condition
that links the micro- and the macroscopic levels finding the relation between the
temperature, the time scales and the dimension of the active degrees of freedom.
12 Bricmont refers to Lanford’s original derivation of Boltzmann’s equation [33].
13 Lanford’s theorem in the case of N hard spheres was extended in [34]. The review [35] nevertheless concludes: Boltzmann’s 1872 effort, to conciliate microscopic time-reversible dynamics with
increase of entropy and trend to equilibrium, still remains as a source of challenging mathematical
problems.
14 It is hard to evaluate general statements made here, since the fundamental difference between CM
and QM at the end of the day turns out to be significant.