Transhumanism and epistemology

The author analyzes the main epistemological orientations characterizing the transhumanist movement, by referring to the results of a recent internal survey. He argues that these data imply a sub-optimal communication between the transhumanist movement and the external world, since its utopian reputation is in contrast with the pragmatic approach to science of most transhumanists. Finally, by shifting from a descriptive perspective to a normative one, he proposes "critical scientism" as an acceptable compromise among the different philosophical souls of the movement and, especially, between scientism and postmodernism

Dynamics of coupled oscillator systems in presence of a local potential

We consider a long-range model of coupled phase-only oscillators subject to a local potential and evolving in presence of thermal noise. The model is a non-trivial generalization of the celebrated Kuramoto model of collective synchronization. We demonstrate by exact results and numerics a surprisingly rich long-time behavior, in which the system settles into either a stationary state that could be in or out of equilibrium and supports either global synchrony or absence of it, or, in a time-periodic synchronized state. The system shows both continuous and discontinuous phase transitions, as well as an interesting reentrant transition in which the system successively loses and gains synchrony on steady increase of the relevant tuning parameter.Comment: v2: close to the published versio

Microcanonical solution of the mean-field ϕ4\phi^4 model: comparison with time averages at finite size

We solve the mean-field $\phi^4$ model in an external magnetic field in the microcanonical ensemble using two different methods. The first one is based on Rugh's microcanonical formalism and leads to express macroscopic observables, such as temperature, specific heat, magnetization and susceptibility, as time averages of convenient functions of the phase-space. The approach is applicable for any finite number of particles $N$. The second method uses large deviation techniques and allows us to derive explicit expressions for microcanonical entropy and for macroscopic observables in the $N \to\infty$ limit. Assuming ergodicity, we evaluate time averages in molecular dynamics simulations and, using Rugh's approach, we determine the value of macroscopic observables at finite $N$. These averages are affected by a slow time evolution, often observed in systems with long-range interactions. We then show how the finite $N$ time averages of macroscopic observables converge to their corresponding $N\to\infty$ values as $N$ is increased. As expected, finite size effects scale as $N^{-1}$.Comment: 18 pages, 1 figur

Statistical mechanics and dynamics of solvable models with long-range interactions

The two-body potential of systems with long-range interactions decays at large distances as $V(r)\sim 1/r^\alpha$, with $\alpha\leq d$, where $d$ is the space dimension. Examples are: gravitational systems, two-dimensional hydrodynamics, two-dimensional elasticity, charged and dipolar systems. Although such systems can be made extensive, they are intrinsically non additive. Moreover, the space of accessible macroscopic thermodynamic parameters might be non convex. The violation of these two basic properties is at the origin of ensemble inequivalence, which implies that specific heat can be negative in the microcanonical ensemble and temperature jumps can appear at microcanonical first order phase transitions. The lack of convexity implies that ergodicity may be generically broken. We present here a comprehensive review of the recent advances on the statistical mechanics and out-of-equilibrium dynamics of systems with long-range interactions. The core of the review consists in the detailed presentation of the concept of ensemble inequivalence, as exemplified by the exact solution, in the microcanonical and canonical ensembles, of mean-field type models. Relaxation towards thermodynamic equilibrium can be extremely slow and quasi-stationary states may be present. The understanding of such unusual relaxation process is obtained by the introduction of an appropriate kinetic theory based on the Vlasov equation.Comment: 118 pages, review paper, added references, slight change of conten

Long time behavior of quasi-stationary states of the Hamiltonian Mean-Field model

The Hamiltonian Mean-Field model has been investigated, since its introduction about a decade ago, to study the equilibrium and dynamical properties of long-range interacting systems. Here we study the long-time behavior of long-lived, out-of-equilibrium, quasi-stationary dynamical states, whose lifetime diverges in the thermodynamic limit. The nature of these states has been the object of a lively debate, in the recent past. We introduce a new numerical tool, based on the fluctuations of the phase of the instantaneous magnetization of the system. Using this tool, we study the quasi-stationary states that arise when the system is started from different classes of initial conditions, showing that the new observable can be exploited to compute the lifetime of these states. We also show that quasi-stationary states are present not only below, but also above the critical temperature of the second order magnetic phase transition of the model. We find that at supercritical temperatures the lifetime is much larger than at subcritical temperatures.Comment: Submitted to Phys. Rev.

Metastable states in a class of long-range Hamiltonian systems

We numerically show that metastable states, similar to the Quasi Stationary States found in the so called Hamiltonian Mean Field Model, are also present in a generalized model in which $N$ classical spins (rotators) interact through ferromagnetic couplings decaying as $r^{-\alpha}$, where $r$ is their distance over a regular lattice. Scaling laws with $N$ are briefly discussed.Comment: Latex 2e, 11 pages, 3 eps figures, contributed paper to the conf. "NEXT 2001", 23-30 May 2001, Cagliari (Italy), submitted to Physica