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Special Issue "Arrow of Time"

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A special issue of Entropy (ISSN 1099-4300).

Deadline for manuscript submissions: closed (15 January 2012)

Special Issue Editor

Guest Editor
Prof. Craig Callender

Professor of Philosophy, University of California, San Diego, 9500 Gilman Drive, La Jolla, CA 92093, USA
Website | E-Mail
Interests: time in physics; second law; foundations of thermodynamics and statistical mechanics; the direction of time; philosophy of science; interpretation of quantum mechanics

Special Issue Information

Dear Colleagues,

Problems connected to the arrow of time remain some of science's largest mysteries. Perhaps because the direction of time plays such a large role in our own lives we maintain a persistent interest in any science that distinguishes the past from future in a robust manner. Whatever the reason, there are many open and fascinating questions associated with the arrow of time in and across many sciences. In statistical mechanics, Boltzmann and many other greats of physics tackled the origins of thermodynamic entropy increase. This puzzle remains, but so do many comparable ones concerning the radiation arrow, cosmological arrow, psychological arrow, and more. What are the origins of these arrows? How are they affected when (e.g.) gravity is taken into account?  How do they relate to one another? We hope for progress on these and other questions in this issue.

Prof. Craig Callender
Guest Editor

Keywords

  • second law of thermodynamics
  • irreversibility
  • time reversal invariance
  • temporal asymmetries
  • initial conditions
  • entropy
  • reversibility paradox

Published Papers (8 papers)

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Research

Open AccessArticle Experimental Test of the “Special State” Theory of Quantum Measurement
Entropy 2012, 14(4), 665-686; doi:10.3390/e14040665
Received: 25 December 2011 / Revised: 21 March 2012 / Accepted: 26 March 2012 / Published: 2 April 2012
Cited by 3 | PDF Full-text (335 KB) | HTML Full-text | XML Full-text
Abstract
An experimental test of the “special state” theory of quantum measurement is proposed. It should be feasible with present-day laboratory equipment and involves a slightly elaborated Stern–Gerlach setup. The “special state” theory is conservative with respect to quantum mechanics, but radical with respect
[...] Read more.
An experimental test of the “special state” theory of quantum measurement is proposed. It should be feasible with present-day laboratory equipment and involves a slightly elaborated Stern–Gerlach setup. The “special state” theory is conservative with respect to quantum mechanics, but radical with respect to statistical mechanics, in particular regarding the arrow of time. In this article background material is given on both quantum measurement and statistical mechanics aspects. For example, it is shown that future boundary conditions would not contradict experience, indicating that the fundamental equal-a-priori-probability assumption at the foundations of statistical mechanics is far too strong (since future conditioning reduces the class of allowed states). The test is based on a feature of this theory that was found necessary in order to recover standard (Born) probabilities in quantum measurements. Specifically, certain systems should have “noise” whose amplitude follows the long-tailed Cauchy distribution. This distribution is marked by the occasional occurrence of extremely large signals as well as a non-self-averaging property. The proposed test is a variant of the Stern–Gerlach experiment in which protocols are devised, some of which will require the presence of this noise, some of which will not. The likely observational schemes would involve the distinction between detection and non-detection of that “noise”. The signal to be detected (or not) would be either single photons or electric fields (and related excitations) in the neighborhood of the ends of the magnets. Full article
(This article belongs to the Special Issue Arrow of Time)
Open AccessArticle Modeling Time’s Arrow
Entropy 2012, 14(4), 614-629; doi:10.3390/e14040614
Received: 2 February 2012 / Revised: 13 March 2012 / Accepted: 19 March 2012 / Published: 23 March 2012
Cited by 3 | PDF Full-text (236 KB) | HTML Full-text | XML Full-text
Abstract
Quantum gravity, the initial low entropy state of the Universe, and the problem of time are interlocking puzzles. In this article, we address the origin of the arrow of time from a cosmological perspective motivated by a novel approach to quantum gravitation. Our
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Quantum gravity, the initial low entropy state of the Universe, and the problem of time are interlocking puzzles. In this article, we address the origin of the arrow of time from a cosmological perspective motivated by a novel approach to quantum gravitation. Our proposal is based on a quantum counterpart of the equivalence principle, a general covariance of the dynamical phase space. We discuss how the nonlinear dynamics of such a system provides a natural description for cosmological evolution in the early Universe. We also underscore connections between the proposed non-perturbative quantum gravity model and fundamental questions in non-equilibrium statistical physics. Full article
(This article belongs to the Special Issue Arrow of Time)
Open AccessArticle Temporal Asymmetry, Entropic Irreversibility, and Finite-Time Thermodynamics: From Parmenides–Einstein Time-Reversal Symmetry to the Heraclitan Entropic Arrow of Time
Entropy 2012, 14(3), 407-455; doi:10.3390/e14030407
Received: 3 February 2012 / Accepted: 17 February 2012 / Published: 28 February 2012
Cited by 6 | PDF Full-text (356 KB) | HTML Full-text | XML Full-text
Abstract
In this paper, we combine the two universalisms of thermodynamics and dynamical systems theory to develop a dynamical system formalism for classical thermodynamics. Specifically, using a compartmental dynamical system energy flow model we develop a state-space dynamical system model that captures the key
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In this paper, we combine the two universalisms of thermodynamics and dynamical systems theory to develop a dynamical system formalism for classical thermodynamics. Specifically, using a compartmental dynamical system energy flow model we develop a state-space dynamical system model that captures the key aspects of thermodynamics, including its fundamental laws. In addition, we establish the existence of a unique, continuously differentiable global entropy function for our dynamical system model, and using Lyapunov stability theory we show that the proposed thermodynamic model has finite-time convergent trajectories to Lyapunov stable equilibria determined by the system initial energies. Finally, using the system entropy, we establish the absence of Poincaré recurrence for our thermodynamic model and develop clear and rigorous connections between irreversibility, the second law of thermodynamics, and the entropic arrow of time. Full article
(This article belongs to the Special Issue Arrow of Time)
Open AccessArticle Bumps on the Road to Here (from Eternity)
Entropy 2012, 14(3), 390-406; doi:10.3390/e14030390
Received: 20 December 2011 / Revised: 14 February 2012 / Accepted: 16 February 2012 / Published: 23 February 2012
Cited by 2 | PDF Full-text (448 KB) | HTML Full-text | XML Full-text
Abstract
In his recent book, From Eternity to Here, and in other more technical papers, Sean Carroll (partly in collaboration with Jennifer Chen) has put forward an intriguing new way to think about the origin of the Universe. His approach, in a nutshell,
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In his recent book, From Eternity to Here, and in other more technical papers, Sean Carroll (partly in collaboration with Jennifer Chen) has put forward an intriguing new way to think about the origin of the Universe. His approach, in a nutshell, is to raise certain worries about a standard Boltzmannian picture of statistical mechanics, and to present certain commitments that he thinks we ought to hold—commitments that the standard picture doesn’t share. He then proposes a cosmological model—one that purports to give us insight into what sort of process brought about the “initial state” of the universe—that can uniquely accommodate those commitments. The conclusion of Carroll’s argument is that statistical mechanical reasoning provides grounds for provisionally accepting that cosmological model. My goal in this paper is to reconstruct and critically assess this proposal. I argue that “statistical cosmology” requires a careful balance of philosophical intuitions and commitments against technical, scientific considerations; how much stock we ought to place in these intuitions and commitments should depend on where they lead us—those that lead us astray scientifically might well be in need of philosophical re‑examination. Full article
(This article belongs to the Special Issue Arrow of Time)
Open AccessArticle Interventionism in Statistical Mechanics
Entropy 2012, 14(2), 344-369; doi:10.3390/e14020344
Received: 13 January 2012 / Revised: 9 February 2012 / Accepted: 9 February 2012 / Published: 17 February 2012
PDF Full-text (135 KB) | HTML Full-text | XML Full-text
Abstract
I defend the idea that the fact that no system is entirely isolated (“Interventionism”) can be used to explain the successful use of the microcanonical distribution in statistical mechanics. The argument turns on claims about what is needed for an adequate explanation of
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I defend the idea that the fact that no system is entirely isolated (“Interventionism”) can be used to explain the successful use of the microcanonical distribution in statistical mechanics. The argument turns on claims about what is needed for an adequate explanation of this fact: I argue in particular that various competing explanations do not meet reasonable conditions of adequacy, and that the most striking lacuna in Interventionism—its failure to explain the “arrow of time”—is no real defect. Full article
(This article belongs to the Special Issue Arrow of Time)
Open AccessArticle Classical and Quantum Models in Non-Equilibrium Statistical Mechanics: Moment Methods and Long-Time Approximations
Entropy 2012, 14(2), 291-322; doi:10.3390/e14020291
Received: 21 December 2011 / Revised: 25 January 2012 / Accepted: 9 February 2012 / Published: 15 February 2012
Cited by 1 | PDF Full-text (497 KB) | HTML Full-text | XML Full-text
Abstract
We consider non-equilibrium open statistical systems, subject to potentials and to external “heat baths” (hb) at thermal equilibrium at temperature T (either with ab initio dissipation or without it). Boltzmann’s classical equilibrium distributions generate, as Gaussian weight functions in momenta, orthogonal polynomials in
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We consider non-equilibrium open statistical systems, subject to potentials and to external “heat baths” (hb) at thermal equilibrium at temperature T (either with ab initio dissipation or without it). Boltzmann’s classical equilibrium distributions generate, as Gaussian weight functions in momenta, orthogonal polynomials in momenta (the position-independent Hermite polynomialsHn’s). The moments of non-equilibrium classical distributions, implied by the Hn’s, fulfill a hierarchy: for long times, the lowest moment dominates the evolution towards thermal equilibrium, either with dissipation or without it (but under certain approximation). We revisit that hierarchy, whose solution depends on operator continued fractions. We review our generalization of that moment method to classical closed many-particle interacting systems with neither a hb nor ab initio dissipation: with initial states describing thermal equilibrium at T at large distances but non-equilibrium at finite distances, the moment method yields, approximately, irreversible thermalization of the whole system at T, for long times. Generalizations to non-equilibrium quantum interacting systems meet additional difficulties. Three of them are: (i) equilibrium distributions (represented through Wigner functions) are neither Gaussian in momenta nor known in closed form; (ii) they may depend on dissipation; and (iii) the orthogonal polynomials in momenta generated by them depend also on positions. We generalize the moment method, dealing with (i), (ii) and (iii), to some non-equilibrium one-particle quantum interacting systems. Open problems are discussed briefly. Full article
(This article belongs to the Special Issue Arrow of Time)
Open AccessArticle Disentangling Complexity from Randomness and Chaos
Entropy 2012, 14(2), 177-212; doi:10.3390/e14020177
Received: 27 December 2011 / Revised: 26 January 2012 / Accepted: 31 January 2012 / Published: 7 February 2012
Cited by 4 | PDF Full-text (1682 KB) | HTML Full-text | XML Full-text
Abstract
This study aims to disentangle complexity from randomness and chaos, and to present a definition of complexity that emphasizes its epistemically distinct qualities. I will review existing attempts at defining complexity and argue that these suffer from two major faults: a tendency to
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This study aims to disentangle complexity from randomness and chaos, and to present a definition of complexity that emphasizes its epistemically distinct qualities. I will review existing attempts at defining complexity and argue that these suffer from two major faults: a tendency to neglect the underlying dynamics and to focus exclusively on the phenomenology of complex systems; and linguistic imprecisions in describing these phenomenologies. I will argue that the tendency to discuss phenomenology removed from the underlying dynamics is the main root of the difficulties in distinguishing complex from chaotic or random systems. In my own definition, I will explicitly try to avoid these pitfalls. The theoretical contemplations in this paper will be tested on a sample of five models: the random Kac ring, the chaotic CA30, the regular CA90, the complex CA110 and the complex Bak-Sneppen model. Although these modelling studies are restricted in scope and can only be seen as preliminary, they still constitute on of the first attempts to investigate complex systems comparatively. Full article
(This article belongs to the Special Issue Arrow of Time)
Open AccessArticle Fluctuation, Dissipation and the Arrow of Time
Entropy 2011, 13(12), 2024-2035; doi:10.3390/e13122024
Received: 8 November 2011 / Revised: 6 December 2011 / Accepted: 12 December 2011 / Published: 19 December 2011
Cited by 6 | PDF Full-text (556 KB) | HTML Full-text | XML Full-text
Abstract
The recent development of the theory of fluctuation relations has led to new insights into the ever-lasting question of how irreversible behavior emerges from time-reversal symmetric microscopic dynamics. We provide an introduction to fluctuation relations, examine their relation to dissipation and discuss their
[...] Read more.
The recent development of the theory of fluctuation relations has led to new insights into the ever-lasting question of how irreversible behavior emerges from time-reversal symmetric microscopic dynamics. We provide an introduction to fluctuation relations, examine their relation to dissipation and discuss their impact on the arrow of time question. Full article
(This article belongs to the Special Issue Arrow of Time)
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