Megascopic Quantum Phenomena
365
theorem implies symmetry broken J-T states and recognizes the individual reacting
molecules. If we have a reaction of the type A + B ← → C (in both directions),
then the left side contains n A + n B −12 phonons, 6 rotons and 6 translons, and the
right side n C phonons, 3 rotons and 3 translons. The number of Goldstone bosons
during the reaction is preserved, and the chemical reaction happens only if 3 rotons
and 3 translons are annihilated and 6 phonons are created, or vice versa. This is a
megascopic irreversible process—a quantum jump from the fragmented Universe,
containing individual molecules A and B, into the whole Universe, where the molecular individuality is lost, and then again in the fragmented Universe with the molecule
C of the same energy as that of A + B in the same configuration at which the reaction
proceeds, or vice versa.
We know well the irreversible nature of chemical reactions, and Santilli was a half
century ago absolutely right with his “no reduction theorem”, see Sect. 2. It means,
that contemporary quantum physics with its reversible equations can never justify
this irreversibility, and therefore is unable to explain a single chemical reaction. It is
able to explain only the physical pre- and postprocesses occurring during reactions,
but not the chemical reactions themselves. Santilli still believes in the microscopic
explanation of chemical reactions, and has proposed an irreversible mathematical
framework for physical equations. We have shown that chemical reactions belong
to the group of megascopic phenomena, where irreversibility descends from the
megascopic quantum jumps, and thus no irreversible equations are necessary.
If physical entropy is assigned to the multitude of equivalent isomeric molecular
ground states there appears another paradox of residual entropy arising from chemistry. One of the first examples of residual entropy was already pointed out by Pauling
to describe water-ice [148]. In water, each oxygen atom is bonded to two hydrogen
atoms. For a large number of water molecules in this configuration, the hydrogen
atoms have a large number of possible configurations that meet the 2-in 2-out rule,
since each oxygen atom must have two ‘near’ (or ‘in’) hydrogen atoms, and two far
(or ‘out’) hydrogen atoms. This freedom exists down to absolute zero. The existence
of these multiple configurations amounts to randomness, or in other words, entropy.
Thus systems that can take multiple configurations at or near absolute zero are said to
have residual entropy. Of course, residual entropy is in strong contradiction with the
third law of thermodynamics that states: the entropy of a perfect crystal of any pure
substance approaches zero as the temperature approaches absolute zero. Here one
might suggest a megascopic solution to this paradox. Realizing, that possible tunnelling between different isomeric configurations of ice is of megascopic origin, i.e.
microscopically inaccessible, then it is convenient to introduce a separate “chemical”
entropy for megascopic processes, so that the physical third law of thermodynamics
remains still valid.
A second example of the illusive violation of the third law of thermodynamics
is the liquid–glass transition with actually a negative residual entropy. There are
several differences between liquid-crystal and liquid–glass transitions. In the first
case the arrangement of atoms and molecules differs from that of a liquid, but in the
second case this arrangement is indistinguishable from it. In the first case there is a
first-order phase transition involving discontinuities in thermodynamic and dynamic
365
theorem implies symmetry broken J-T states and recognizes the individual reacting
molecules. If we have a reaction of the type A + B ← → C (in both directions),
then the left side contains n A + n B −12 phonons, 6 rotons and 6 translons, and the
right side n C phonons, 3 rotons and 3 translons. The number of Goldstone bosons
during the reaction is preserved, and the chemical reaction happens only if 3 rotons
and 3 translons are annihilated and 6 phonons are created, or vice versa. This is a
megascopic irreversible process—a quantum jump from the fragmented Universe,
containing individual molecules A and B, into the whole Universe, where the molecular individuality is lost, and then again in the fragmented Universe with the molecule
C of the same energy as that of A + B in the same configuration at which the reaction
proceeds, or vice versa.
We know well the irreversible nature of chemical reactions, and Santilli was a half
century ago absolutely right with his “no reduction theorem”, see Sect. 2. It means,
that contemporary quantum physics with its reversible equations can never justify
this irreversibility, and therefore is unable to explain a single chemical reaction. It is
able to explain only the physical pre- and postprocesses occurring during reactions,
but not the chemical reactions themselves. Santilli still believes in the microscopic
explanation of chemical reactions, and has proposed an irreversible mathematical
framework for physical equations. We have shown that chemical reactions belong
to the group of megascopic phenomena, where irreversibility descends from the
megascopic quantum jumps, and thus no irreversible equations are necessary.
If physical entropy is assigned to the multitude of equivalent isomeric molecular
ground states there appears another paradox of residual entropy arising from chemistry. One of the first examples of residual entropy was already pointed out by Pauling
to describe water-ice [148]. In water, each oxygen atom is bonded to two hydrogen
atoms. For a large number of water molecules in this configuration, the hydrogen
atoms have a large number of possible configurations that meet the 2-in 2-out rule,
since each oxygen atom must have two ‘near’ (or ‘in’) hydrogen atoms, and two far
(or ‘out’) hydrogen atoms. This freedom exists down to absolute zero. The existence
of these multiple configurations amounts to randomness, or in other words, entropy.
Thus systems that can take multiple configurations at or near absolute zero are said to
have residual entropy. Of course, residual entropy is in strong contradiction with the
third law of thermodynamics that states: the entropy of a perfect crystal of any pure
substance approaches zero as the temperature approaches absolute zero. Here one
might suggest a megascopic solution to this paradox. Realizing, that possible tunnelling between different isomeric configurations of ice is of megascopic origin, i.e.
microscopically inaccessible, then it is convenient to introduce a separate “chemical”
entropy for megascopic processes, so that the physical third law of thermodynamics
remains still valid.
A second example of the illusive violation of the third law of thermodynamics
is the liquid–glass transition with actually a negative residual entropy. There are
several differences between liquid-crystal and liquid–glass transitions. In the first
case the arrangement of atoms and molecules differs from that of a liquid, but in the
second case this arrangement is indistinguishable from it. In the first case there is a
first-order phase transition involving discontinuities in thermodynamic and dynamic