Brussels-Austin theory

[was: The least action principle as a consequence of Maxent]

Juan R. schrieb:
On Sep 28, 12:49 pm, Arnold Neumaier <Arnold.Neuma...@xxxxxxxxxxxx>
wrote:
Juan R. schrieb:

The Brussels-Austin group is the group was leaded by Prigogine. We
informally call the theory the "Brussels-Austin theory". Still a
Google search will return results.


One of the Google results (which compared to your references has
the advantage of being online) is

R.C. Bishop
Brussels-Austin Nonequilibrium Statistical Mechanics: Large Poincare
Systems and Rigged Hilbert Space,
http://www.igpp.de/english/tda/pdf/BrusselsAustin.pdf

Does it contain the essence?


The best way is to follow directly
the authors' literature [2].

This is a very long list. Surely not all of them are equally relevant.
Which references there gives the key to this theory?


Please give more details. What is it about?

The idea fundamental is that Poincare resonances split models into two
large classes: integrable and non-integrable. See [1, 2, 3] and
previous message for details on that follows.

Non-integrable systems need of an extension of dynamics and that
extension deal with phenomena like irreversibility, dissipation, and
so called non-deterministic chaos.

Examples of non-integrable class (called LPS [*] in the theory) are
thermodynamics systems, measurement apparatus in quantum mechanics,
instable particles (fields)...

Regarding collapse, this theory *dinamically* differentiates simple
quantum systems (following Schrödinger equation) from measurement
apparatus (Schrödinger does not apply). The difference finds in the
spectra.

Spectral decomposition for an usual quantum system (e.g. atom):

H = SUM_j |Phi_j> E_j <Phi_j|

Spectral decomposition for a measurement apparatus:

L = SUM_v SUM_alpha |F_alpha^(v)>> Z_alpha^(v) <<TILDE F_alpha^(v)|

Equation of motion for an usual quantum system (e.g. atom):

{PARTIAL |PHI> / PARTIAL t} = H |PHI>

Equation of motion for a measurement apparatus:

{PARTIAL |RHO_B>> / PARTIAL t} = THETA_B |RHO_B>>

with

THETA _B = { LAMBDA_B L {LAMBDA_B}^-1 }

All this looks to me to be the same, apart from a change in notation.


This dynamical distinction is a fundamental point you do not find in
other theories dealing with quantum measurement and collapse.

A reference?

In [2] you can see list of recent published references including best-
seller books like _The End of Certainty, Time, Chaos and the New Laws
of Nature_ for general audiences.

I am interested in a (recent) survey for experts, not in a
laymen's book. Theory is easier to understand if not enclouded
in philosophy for everyone...


Arnold Neumaier

.