[time 245] Discussion of Mackey's work with Huw Price

Stephen P. King (stephenk1@home.com)
Sun, 18 Apr 1999 13:50:34 -0400

>Date: Fri, 06 Feb 1998 11:44:55 -0400
>To: Huw Price <huw@mail.usyd.edu.au>
>From: Stephen Paul King <spking1@mindspring.com>
>Subject: Re: Michael C. Mackey
>In-Reply-To: <v03110700b1005bdaa142@[]>
>References: <>
>Quoting from pg. ix:
>"The central question that this book addresses is the dynamic origin of the Second Law of thermodynamics. Specifially, the goal is to define the 'dynamical' foundation of the evolution of entropy to maximal states. This is accomplished through an application of resent results in ergodic theory to so-called "chaotic" dynamical systems(Lasota and Mackey, 1985; M. C. Mackey, 1989)..."
>The author goes on to define the weak and strong forms of the Second Law.
>pg. x;
> "Chapter 1 defines a thermodynamic system in terms of measure spaces, draws a one to one correspondence between a density and a thermodynamic state and introduces the Boltzmann-gibbs entropy of a density.
> In Chapter 2, using a Maximal Entropy Postulate, it is a simple demonstration that the entropy of a density will assume a maximal value if and only if this density is (in the terminology of Gibbs) either the density of the microcanonical or a generalized canonical ensemble. Then it is shown that the Boltzmann-Gibbs entropy of a density can plausibly be argued to coincide with the thermodynamic entropy S_TD of a system characterized by that density."
>The author goes on to define Markow and Frobenius-Perron operators in these terms and their properties and then "turn(s) to a consideration of the conditions that quarantee the existence of a 'unique' state of thermodynamic equilibrium. The necessary and sufficiennt conditionn for this existance is the property of ergodicity, which may be shared by both invertible and noninvertible systems."
> Mackey then proceds to define and elaborate on the various type of properties that generate entropy in systems including mixing and asymptotic periodicity.
> "Chapter 7 is, in a sense, the core of this work. There it is shown that for there to be a global evolution of entropy to its maximal state of zero (strong form of the Second Law) it is 'necessary and sufficient' that the system have a property known as exactness.
> In a very real way, the results of Chapter 7 raise as many questions as they answer. Though providing totally clear criteria for the global evolution of system entropy, at the same time these criteria suggest that all currently formulated physical laws may not be at the foundation of the thermodynamic behaviour we observe every day of our lives. This is simply because theese laws are formulated as (invertible) dynamical systems, and exactness is a property that only noninvertible systems may display.
> One possibility is that the current invertible, dynamical system statements of physical laws are incorrect and that more appropriate formulations in terms of noninvertible semidynamical systems await discovery. Alternately, other phenomena may mask the operation of these invertible systems so that they appear noninvertible to the observer Chapters 8 - 11 explore this latter possibility."
> I have been studying the work of Cramer that you talk about in your book and been studying the Interaction model in terms of information theory (that is, the energy required to transmit the message is proportional to the communication-theory entropy of the message source) and Vaughn Pratt's "Chu space" formalism to develop a rigorous model for time. Thank you for your time.
>Stephen Paul King
>At 04:20 PM 2/6/98 +1000, you wrote:
>>>Dear Sir.
>>>Are you familiar with the work of Michael C. Mackey (at McGill), namely his
>>>book: Time's Arrow: the Origins of Thermodynamic Behavior, Spr-Verlag, 1992?
>>>Any comment on his results? Thanks for your time.
>>I've heard of this book, but I don't think I've ever looked at it. What's
>>his line?

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