Two-way thermodynamics: Could it really happen?

In previous publications I have suggested that opposite thermodynamic arrows of time could coexist in our universe. This letter responds to the comments of H. D. Zeh (previous letter in this journal). In 2002 a conference took place in Bielefeld, entitled, " The direction of time: The role of reversibil-ity/irreversibility in the study of nature " [1]. In my presentation I spoke about recent work in which I had demonstrated the compatibility of opposite arrows of time for two subsystems within a larger " universe. " As Dieter Zeh explains in his companion article [2], he has reservations about the physical realizability of this phenomenon and our present articles address this issue. However, as a preface to my response to his remarks, I will give a brief review, plus references, to the work that has given rise to this dialog. When this response was originally written I gave it the title, " The slings and arrows. .. whips and scorns of time, " [3], not because of the barbs that Zeh was throwing my way, but quite the opposite, because of a review I had written years ago of the first edition of his book, [4], for Science magazine [5]. Instead of giving it its deserved high praise, I looked for faults, some it turns out of my own invention. So this " response " gives me the opportunity to apologize for that review. 2 Opposite arrows The thesis that the thermodynamic arrow of time follows the cosmological arrow (the universe is expanding) was put forth by Gold about 1960 [6]. My contribution, about 10 years later [7], was to observe that if you wanted to make this case in a logical way, you needed to recognize that the choice of giving initial or final conditions was itself a choice of the arrow (and that you needed to be careful about this in the sort of arguments Gold was offering). So that to establish Gold's thesis one should argue from time-symmetric boundary conditions. For elaboration and references see my book [8], where I do indeed make such arguments. With this perspective, the thermodynamic arrow of time becomes a consequence of the cosmological geometry rather than an independent physical input. This leads to a problem that can be posed purely mathematically. We know that if a low entropy macroscopic state is given as an initial condition, the entropy will increase. (The …