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E. J. Brändas
domain the corresponding calculations have been labelled ab initio, promoting the
important conception of correlation energies as benchmarks for quantum accuracy
and scaling. This first principle method
10 should be contrasted with the less time
consuming and easier-to-perform semi-empirical approaches that provide important,
but less reliable theoretical answers, adding supplementary epistemic contextual data
to the table.
These distinctions become important when probing the concepts that go into
the sub-dynamics picture. Developing non-equilibrium thermodynamic formulations
prompted Prigogine to infer two distinct notions of irreversibility, extrinsic and intrinsic. Basically, the former exemplifies open systems coupled to its surroundings, while
the latter does not indicate any environment whatsoever therefore suggesting a more
fundamental hypothesis of irreversibility as a viable physical law. This view was
central to Ilya Prigogine, since it imparts that irreversibility is in the details of the
interactions, rather than being related to the singularity at the origin of our universe.
A detailed examination of this principle has been given by Atmanspacher,
Bishop
11 and Amann [16], see also [28, 29], where they appraise the two mentioned kinds of irreversibility based on ontic and epistemic descriptions. Since ontic
states usually refer to closed systems which are empirically inaccessible, open systems are clearly different, the latter suggesting the depiction of epistemic states. In
other words, Prigogine’s objective was to ground onticity, if possible, on a fundamental principle, where in contrast to Monod’s Chance and Necessity [23] being
and becoming should set in motion a new culture about how we understand and
experience Nature and its laws [27].
The distinction between extrinsic and intrinsic is not without problem. For
instance, a system undergoing radioactive decay, is initially closed with no environment explicitly revealed. Nevertheless, there exists a prepared low entropy initial
condition that is embedded in the time span of nucleo-synthesis, which then relates
temporal irreversibility with the initial singularity of the universe. A similar problem
seems to appear in the case of a box with all the particles collected in one corner.
However, here there is no telling whether this initial condition was crafted by outside intervention or by an improbable fluctuation evolved in agreement with time
reversible dynamical laws. This uncertainty prompts another fundamental query,
viz. does there exist a law, i.e. an unavoidable deficiency rule causing a natural
loss of information effectively accompanying sub-dynamics compatible with broken
temporal symmetry [30]. We will return to this question further below.
As cited above the critics in Refs. [16, 28, 29] question some of the interpretations and general conclusions of the steps that formed Prigogine’s world-view, but
still there have not so far been given any serious objections to the derived and applied
mathematical formulations, such as those given from classical chaos theory to the
10 The debate whether the Nobel Prize awarded work on density functional theory, DFT, should be
considered ab initio will not be discussed here. Yet, DFT is definitely epistemic in nature.
11 Bishop has analysed the work of the Brussels-Austin Group [29] with particular focus on the
definitions and mathematical extensions to rigged Hilbert spaces and its applications to concrete
mathematical systems.
E. J. Brändas
domain the corresponding calculations have been labelled ab initio, promoting the
important conception of correlation energies as benchmarks for quantum accuracy
and scaling. This first principle method
10 should be contrasted with the less time
consuming and easier-to-perform semi-empirical approaches that provide important,
but less reliable theoretical answers, adding supplementary epistemic contextual data
to the table.
These distinctions become important when probing the concepts that go into
the sub-dynamics picture. Developing non-equilibrium thermodynamic formulations
prompted Prigogine to infer two distinct notions of irreversibility, extrinsic and intrinsic. Basically, the former exemplifies open systems coupled to its surroundings, while
the latter does not indicate any environment whatsoever therefore suggesting a more
fundamental hypothesis of irreversibility as a viable physical law. This view was
central to Ilya Prigogine, since it imparts that irreversibility is in the details of the
interactions, rather than being related to the singularity at the origin of our universe.
A detailed examination of this principle has been given by Atmanspacher,
Bishop
11 and Amann [16], see also [28, 29], where they appraise the two mentioned kinds of irreversibility based on ontic and epistemic descriptions. Since ontic
states usually refer to closed systems which are empirically inaccessible, open systems are clearly different, the latter suggesting the depiction of epistemic states. In
other words, Prigogine’s objective was to ground onticity, if possible, on a fundamental principle, where in contrast to Monod’s Chance and Necessity [23] being
and becoming should set in motion a new culture about how we understand and
experience Nature and its laws [27].
The distinction between extrinsic and intrinsic is not without problem. For
instance, a system undergoing radioactive decay, is initially closed with no environment explicitly revealed. Nevertheless, there exists a prepared low entropy initial
condition that is embedded in the time span of nucleo-synthesis, which then relates
temporal irreversibility with the initial singularity of the universe. A similar problem
seems to appear in the case of a box with all the particles collected in one corner.
However, here there is no telling whether this initial condition was crafted by outside intervention or by an improbable fluctuation evolved in agreement with time
reversible dynamical laws. This uncertainty prompts another fundamental query,
viz. does there exist a law, i.e. an unavoidable deficiency rule causing a natural
loss of information effectively accompanying sub-dynamics compatible with broken
temporal symmetry [30]. We will return to this question further below.
As cited above the critics in Refs. [16, 28, 29] question some of the interpretations and general conclusions of the steps that formed Prigogine’s world-view, but
still there have not so far been given any serious objections to the derived and applied
mathematical formulations, such as those given from classical chaos theory to the
10 The debate whether the Nobel Prize awarded work on density functional theory, DFT, should be
considered ab initio will not be discussed here. Yet, DFT is definitely epistemic in nature.
11 Bishop has analysed the work of the Brussels-Austin Group [29] with particular focus on the
definitions and mathematical extensions to rigged Hilbert spaces and its applications to concrete
mathematical systems.