Re: Time Arrows (Prigogine)

From: Amara Graps (
Date: Mon Jan 22 2001 - 10:42:06 MST

From: scerir <>, Sun, 21 Jan 2001:
> Time Arrow(s)

I wrote the following some years ago to the sci.astro newsgroup. I thought
that some people here might be interested in seeing a repost to this
list, since Prigogine's work is relevant to the topic of Time's Arrows.


Newsgroups: sci.astro
From: (Amara Graps)
Subject: Re: Prigogine
Date: Wed, 16 Jul 1997 08:39:39 GMT

Ryan Aebig <> writes:

>Could anyone tell me in layman terms what he discovered? Apparently he's
>come up with a way to combine statistical and Newtonian physics, so that
>irreversible systems now can be reversed (ie friction and time's arrow)

Prigogine won the Nobel Prize in 1977 for his work in the
thermodynamics of nonequilibrium systems.

Prigogine is primarily a chemist. He was well established in his field
20 years ago, so what he's done since then, is branch out into related
areas. As I understand it, his main discovery has been the discovery
of "chemical clocks." These are chemical reactions that oscillate in a
very regular and precise way. Prigogine predicted that they should
exist from a theoretical chemistry standpoint several decades ago. In
the late 1950's, one of his research group came back from a visit with
a colleague in Russia, announcing that they had a chemical reaction
that did just what Prigogine predicted. The reaction is now known as
the Belousov-Zhabotininskii reaction and it is the oxidation of citric
acid by potassium bromate catalyzed by the ceric-cerous ion couple.

To Prigogine, irreversibility is a fundamental property of
physics. Prigogine proposes that entropy production is part of an
operator (operators map functions onto functions), and time is an
operator. And that the time that we are all familiar with from
classical mechanics is just an ensemble average of this operator with
a state vector. I.e. "ordinary" time is an average over his new
time operator. And that "age" is DEpendent of the distibution.

So what does that mean about operators..? Let's say that we wish to
know the time evolution of a system. In both quantum mechanics and
classical mechanics, the Hamiltonian operator determines how the
system will evolve in time. The evolution that we are all familiar
with is a reversible and deterministic evolution (We can say that the
reversible change of a wave function that represents the quantum
system corresponds to a reversible motion along a trajectory that
represents the classical system.) The wave function or trajectory
represents the maximum knowledge of the system.

Prigogine has incorporated reversible and irreversible parts into a
new microscopic equation/description. The equation contains an
operator analogous to the Hamiltonian, that is a new "time evolution
operator" that now can drive the system to both equilibrium or
nonequilibrium states. Entropy is produced by the even part of the new
time evolution operator and he has defined an operator for that.

An example that Prigogine gives looks at the conventional and his
unconventional determination of energy levels in a quantum system. In
the conventional quantum mechanics, both the energy levels and the
time evolution of them are determined by the same quantity: the
Hamiltonian operator. Prigogine's method allows him to use two
different operators: the time operator for time evolution and another
operator (a "superoperator" that can act on other operators) to
determine the energy levels. So in this way, instead of having the
"particle" and the "interaction" (conventional view), we have the
physical _process_ that contains electrons, photons, etc. that drive
the total system. This process is "real" and cannot be "transformed"
away by any change of representation.

Or another way to look at it: the classical order says particles come
first and the Second Law of Thermodynamics comes later, while
Prigogine says that we must _first_ introduce the Second Law before
being able to define the entities.

Another one of Prigigine's main themes is that nonlinear interactions
frequently lead to order (which he calls "dissipative structures")
through fluctuations. A dissipative structure is order visible on a
macroscale which can exchange energy with the outside world. In
particular, if the system is in a far-from-equilibrium-state this can

In fact, in Prigogine's view, we can now recognize ourselves as a kind
of evolved form of dissipative structure, and we can justify, in an
objective way, the distinction between the future and the past. How?
The time symmetry is broken in the following way: the existence of
irreversible processes on the microscopic level through kinetic
equations violates the symmetry of the canonical equations. And
dissipative structures may, in turn, break the symmetries of

I don't know if I managed to put this in layman's terms. His theory is
very mathematical. But I think this is cool stuff.

You can find out more about Prigogine's ideas in the books: _Order Out
of Chaos_ (few or no equations) and _From Being to Becoming_ (very
technical, but the same subject matter).


Amara Graps email:
Computational Physics vita: finger
Multiplex Answers URL:
"Sometimes I think I understand everything. Then I regain
consciousness." --Ashleigh Brilliant

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