'The arrow of time' refers to the curious asymmetry that distinguishes the future from the past. Reversing the Arrow of Time argues that there is an intimate link between the symmetries of 'time itself' and time reversal symmetry in physical theories, which has wide-ranging implications for both physics and its philosophy. This link helps to clarify how we can learn about the symmetries of our world, how to understand the relationship between symmetries and what is real, and how to overcome (...) pervasive illusions about the direction of time. Roberts explains the significance of time reversal in a way that intertwines physics and philosophy, to establish what the arrow of time means and how we can come to know it. This book is both mathematically and philosophically rigorous yet remains accessible to advanced undergraduates in physics and the philosophy of physics. This title is also available as Open Access on Cambridge Core. (shrink)

To model the organization of levels' of cortical dynamics, at least some general scheme for hierarchy, functional diversity, and proper intrinsic control must be provided. Rhythmic control forces the system to iterate its state by short trajectories, which makes it much more stable and predictable without discarding the desirable ability of chaotic systems to make rapid phase transitions. Rhythmic control provides a fundamentally different systems dynamics, one not provided by models that allow the emergence of continuous trajectories in the systems (...) state space. (shrink)

Two hypotheses concerning nonlinear elements in complex systems are contrasted: that neurons, intrinsically unstable, are stabilized through embedding in networks and populations; and, conversely, that cortical neurons are intrinsically stable, but are destabilized through embedding in cortical populations and corticostriatal feedback systems. Tests are made by piecewise linearization of nonlinear dynamics at nonequilibriumoperating points, followed by linear stability analysis.

A new probabilistic-informational concept, earlier constructed by Mugur-Schächter, is further developed. Associated with Jaynes's principle, this concept permits one to define a measure for the distance between the state of a system evolving under stable constraints and the equilibrium with these constraints. An illustration is given for a gas evolving in a thermostated box. It appears that the free energy of the gas estimates the distance to equilibrium, the estimation being defined in abstract informational-probabilistic terms.

Dynamic systems theory offers conceptual andmathematical tools for describing the performance ofneural systems at very different levels oforganization. Three aspects of the dynamic paradigmare discussed, namely neural rhythms, neural andmental development, and macroscopic brain theories andmodels.

Roughly speaking, classical statistical physics is the branch of theoretical physics that aims to account for the thermal behaviour of macroscopic bodies in terms of a classical mechanical model of their microscopic constituents, with the help of probabilistic assumptions. In the last century and a half, a fair number of approaches have been developed to meet this aim. This study of their foundations assesses their coherence and analyzes the motivations for their basic assumptions, and the interpretations of their central concepts. (...) The most outstanding foundational problems are the explanation of time-asymmetry in thermal behaviour, the relative autonomy of thermal phenomena from their microscopic underpinning, and the meaning of probability. A more or less historic survey is given of the work of Maxwell, Boltzmann and Gibbs in statistical physics, and the problems and objections to which their work gave rise. Next, we review some modern approaches to (i) equilibrium statistical mechanics, such as ergodic theory and the theory of the thermodynamic limit; and to (ii) non-equilibrium statistical mechanics as provided by Lanford's work on the Boltzmann equation, the so-called Bogolyubov-Born-Green-Kirkwood-Yvon approach, and stochastic approaches such as `coarse-graining' and the `open systems' approach. In all cases, we focus on the subtle interplay between probabilistic assumptions, dynamical assumptions, initial conditions and other ingredients used in these approaches. (shrink)

For some years there has been a controversy about whether brain state variables such as EEG or neuronal spike trains exhibit chaotic behaviour. Wright & Liley claim that the local dynamics measured by spike trains or local field potentials exhibit chaotic behaviour, but global measures like EEG should be governed by linear dynamics. We propose a different scheme. Based on simulation studies and various experiments, we suggest that the pointwise dimension of EEG time series may provide some valuable information about (...) underlying neuronal generators. (shrink)

We focus on one aspect of Wright & Liley's target article: the linearity of the EEG. According to the authors, some nonlinear models of the cortex can be reduced (approximated) to the linear case at the millimetric scale. We argue here that the statement about the linear character of EEG is too strong and that EEG exhibits nonlinear features which cannot be ignored.

Some dichotomies related to modeling electrocortical activities are analyzed. Attractor neural networks versus biologically motivated models, near-equilibrium versus nonequilibrium processes, linear and nonlinear dynamics, stochastic and chaotic patterns, local and global scale simulation of cortical activities are discussed.

The network model of EEG formation has revealed a unified mechanism for disparate EEG phenomena: for various reactions as well as for ontogenetic and phylogenetic differences. EEG rhythmicity was shown to be an external manifestation of the functioning of the intracortical stabilizing system which provides normal informational operations in the cerebral cortex.

Although this is an impressive piece of modeling work, I worry that the two models that Wright & Liley have created do not yet provide us with useful empirical information regarding brain processing.

There is some complementarity of models for the origin of the electroencephalogram (EEG) and neural network models for information storage in brainlike systems. From the EEG models of Freeman, of Nunez, and of the authors' group we argue that the wavelike processes revealed in the EEG exhibit linear and near-equilibrium dynamics at macroscopic scale, despite extremely nonlinear – probably chaotic – dynamics at microscopic scale. Simulations of cortical neuronal interactions at global and microscopic scales are then presented. The simulations depend (...) on anatomical and physiological estimates of synaptic densities, coupling symmetries, synaptic gain, dendritic time constants, and axonal delays. It is shown that the frequency content, wave velocities, frequency/wavenumber spectra and response to cortical activation of the electrocorticogram (ECoG) can be reproduced by a “lumped” simulation treating small cortical areas as single-function units. The corresponding cellular neural network simulation has properties that include those of attractor neural networks proposed by Amit and by Parisi. Within the simulations at both scales, sharp transitions occur between low and high cell firing rates. These transitions may form a basis for neural interactions across scale. To maintain overall cortical dynamics in the normal low firing-rate range, interactions between the cortex and the subcortical systems are required to prevent runaway global excitation. Thus, the interaction of cortex and subcortex via corticostriatal and related pathways may partly regulate global dynamics by a principle analogous to adiabatic control of artificial neural networks. (shrink)

From 1873 to 1878, the American physicist Josiah Willard Gibbs offered to the scientific community three great articles that proved to be a milestone for the science of thermodynamics. On the other hand, between 1886 and 1896, the French physicist Pierre Maurice Marie Duhem translated thermodynamics into the language of Lagrange’s analytical mechanics. At the same time, he expanded its scope to include thermal phenomena, electromagnetic phenomena, and all kinds of irreversible processes. Duhem formulated a version of thermodynamics characterized by (...) the conceptual unification of mechanics, physics, and chemistry. Overall, the work of both physicists on thermodynamics is tremendous, full of axioms, theorems, corollaries, proofs, and hundreds of equations. Therefore, it would be a utopian aim to provide a short analysis of their work. Instead, the present study will attempt to give a brief outline of the main tools and concepts used by the two physicists. I will argue that each scientist approaches thermodynamics in a new and unique way, which reveals their scientific styles as reflected in their personalities, the writing styles, their behavior toward publicity, and their inclination for publication. Finally, I will examine the influence of their theories on the development of chemical thermodynamics. (shrink)

We outline fresh findings that show that our macroscopic electrocorticographic (ECoG) simulations can account for synchronous multiunit pulse oscillations at separate, simultaneously activated cortical sites and the associated gamma-band ECoG activity. We clarify our views on the approximations of dynamic class applicable to neural events at macroscopic and microscopic scales, and the analogies drawn to classes of ANN behaviour. We accept the need to introduce memory processes and detailed anatomical and physiological information into any future developments of our simulations. On (...) the issue of intrinsic cortical stability and the role of extrinsic fibre systems in maintaining stability, we argue that this position is not in extreme contradiction to those of our commentators, and that the mechanisms implicit in our simulations' properties imply rich computational possibilities. We discuss some of the reasons for and against the existence of significant global resonances in the brain and explain why such behaviour appears absent in our simulations. Last, we discuss other phenomena, such as rhythmic driving of the cortex, which have not yet been introduced into our models, and indicate lines for future development of the simulations. (shrink)

The unification of microscopic and macroscopic models of brain behaviour is of paramount importance and Wright & Liley's target article provides some important groundwork. In this commentary, I propose that a useful approach for the future is to incorporate a developmental perspective into such models. This may be an important constraint, providing a key to understanding the nature of macroscopic measures of brain function such as functional measures like ERP.

Standard descriptions of thermodynamically reversible processes attribute contradictory properties to them: they are in equilibrium yet still change their state. Or they are comprised of non-equilibrium states that are so close to equilibrium that the difference does not matter. One cannot have states that both change and no not change at the same time. In place of this internally contradictory characterization, the term “thermodynamically reversible process” is here construed as a label for a set of real processes of change involving (...) only non-equilibrium states. The properties usually attributed to a thermodynamically reversible process are recovered as the limiting properties of this set. No single process, that is, no system undergoing change, equilibrium or otherwise, carries those limiting properties. The paper concludes with an historical survey of characterizations of thermodynamically reversible processes and a critical analysis of their shortcomings. (shrink)

Wright & Liley provide an advance in addressing the interaction of multiple scales of processing in the brain. It should address in more detail the biological evidence that underlies the models it proposes to replace.

Simulation of brain dynamics requires the use of accurate empirical data. This commentary points out major errors in some of the empirical data used in Wright & Laley's simulation. The simulation is quantitatively very different from the real cortex, and may also have important qualitative differences.

A purely probabilistic-informational model of evolutions is sketched, basically free of any assumption concerning the nature and structure of the evolving system but apt to incorporatea posteriori any such assumptions needed for application to a specified evolution. The model produces an abstract extension of the second principle of thermodynamics. It also leads to an outline of a typology of irreversible evolutions.

We present simulation results of an olfactory cortex model complementing the results presented in Wright & Liley's target article. We show how the cortical dynamics as expressed in EEG can be regulated by neuromodulation and discuss how the system can attain global stability without cortical-subcortical interaction, as presumed necessary by Wright & Liley. Network structure is shown to be crucial.

The results of two recent articles expanding the Gibbs variational principle to encompass all of statistical mechanics, in which the role of external sources is made explicit, are utilized to further explicate the theory. Representative applications to nonequilibrium thermodynamics and hydrodynamics are presented, describing several fundamental processes, including hydrodynamic fluctuations. A coherent description of macroscopic relaxation dynamics is provided, along with an exemplary demonstration of the approach to equilibrium in a simple fluid.

Multiscale dynamics, linear approximations, global boundary conditions, experimental verification, and global influences on local cell assemblies are considered in the context of Wright & Liley's work. W&L provide a nice introduction to these issues and a reasonable simulation of intermediate scale dynamics, but the model does not adequately simulate combined local and global processes.

I would like to emphasize the significance of chaotic dynamics at both local and macroscopic levels in the cortex. The basic notions dealt with in this commentary will be noise-induced order, chaotic “itinerancy” and dissipative structure. Wright & Laley's theory would be partially misleading, since emergent nonlinearity rather than the linearity at even a macroscopic level can actually subserve cortical functions.

According to Whitehead, nature is disclosed to mind by an ensemble of events characterized by unobservable hidden intrinsic factors (e.g., mass, gravitation) and observable extrinsic factors (e.g., motion, density). Mass is not the substratum of dynamics. It implies spatial extension and temporal duration, which are both necessary conditions of observable natural phenomena. Therefore, an instant, deprived of duration, is immeasurable. Whitehead’s claims on mass, space, and time corroborate Verlinde’s alternative conception of quantum gravitation. Within the de Sitter space-time, this conception (...) starts from the competition of the short distance degrees of freedom of the Ryn-Takanayagi tensor with long-distance thermalized excitations. This enables the creation of a baryonic mass and a decrease in de Sitter entropy. The memory effect of the original baryon creation leads to gravitation and the production of extensive thermodynamic entropy. However, the baryon production shrinks, and the dissipating space-time transforms into a space-timeless cold sink with an accompanying strong contracting memory effect. This is equivalent to the alternate motion of a giant Carnot engine, where the heat source and sink energy exchange produce the eternal periodic dynamics of the Universe. This suggests that the Universe did not start from Big Bang but oscillated eternally as a Big Bounce Universe. (shrink)

Wright & Liley contrast their theory that the global dynamics of the EEG are linear with that of Freeman, who hypothesizes an EEG governed by (nonlinear) deterministic-chaotic dynamics. A “call for further discussion” on the part of the authors is made as to how either theory fits with experimental findings indicating that EEG dynamics are non-linear but stochastic.

Event-related potentials (ERPs) – neglected almost entirely by Wright & Liley – allow objective investigation of information processing in the brain. The application of chaos theory to such an analysis broadens this possibility. Through the use of the point correlation dimension (PD2) accurate dimensional analysis of different Event-Related Potential components such as the P3 wave is possible.

The work in progress reported by Wright & Liley shows great promise, primarily because of their experimental and simulation paradigms. However, their tentative conclusion that macroscopic neocortex may be considered (approximately) a linear near-equilibrium system is premature and does not correspond to tentative conclusions drawn from other studies of neocortex.

Does the Wright & Liley model predict: (1) that subdural and hippocampal EEGs coherence tend to rise and fall in parallel for many frequencies, (2) that it is locally high or low within 10mm and falls steeply on average or, (3) that it is in constant flux, mostly rising and falling within 5–15 sec?

Some concepts relating to learned, structured functioning of local modules in neocortex are clarified in order to ensure that the integration from the small scale to the global attempted by Wright & Liley does not miss the target.