Quantum Macrostates, Equivalence of Ensembles and an H-Theorem

Before the thermodynamic limit, macroscopic averages need not commute for a quantum system. As a consequence, aspects of macroscopic fluctuations or of constrained equilibrium require a careful analysis, when dealing with several observables. We propose an implementation of ideas that go back to John von Neumann's writing about the macroscopic measurement. We apply our scheme to the relation between macroscopic autonomy and an H-theorem, and to the problem of equivalence of ensembles. In particular, we show how the latter is related to the asymptotic equipartition theorem. The main point of departure is an expression of a law of large numbers for a sequence of states that start to concentrate, as the size of the system gets larger, on the macroscopic values for the different macroscopic observables. Deviations from that law are governed by the entropy.Comment: 16 pages; v1 -> v2: Sec. 3 slightly rewritten, 2 references adde

Irreversible thermodynamics of open chemical networks I: Emergent cycles and broken conservation laws

In this and a companion paper we outline a general framework for the thermodynamic description of open chemical reaction networks, with special regard to metabolic networks regulating cellular physiology and biochemical functions. We first introduce closed networks "in a box", whose thermodynamics is subjected to strict physical constraints: the mass-action law, elementarity of processes, and detailed balance. We further digress on the role of solvents and on the seemingly unacknowledged property of network independence of free energy landscapes. We then open the system by assuming that the concentrations of certain substrate species (the chemostats) are fixed, whether because promptly regulated by the environment via contact with reservoirs, or because nearly constant in a time window. As a result, the system is driven out of equilibrium. A rich algebraic and topological structure ensues in the network of internal species: Emergent irreversible cycles are associated to nonvanishing affinities, whose symmetries are dictated by the breakage of conservation laws. These central results are resumed in the relation $a + b = s^Y$ between the number of fundamental affinities $a$, that of broken conservation laws $b$ and the number of chemostats $s^Y$. We decompose the steady state entropy production rate in terms of fundamental fluxes and affinities in the spirit of Schnakenberg's theory of network thermodynamics, paving the way for the forthcoming treatment of the linear regime, of efficiency and tight coupling, of free energy transduction and of thermodynamic constraints for network reconstruction.Comment: 18 page

Marching to a different drummer : a cross-cultural comparison of young adolescents who challenge gender norms

Purpose: Little is known about how gender norms regulate adolescents' lives across different cultural settings. This study aims to illustrate what is considered as violating gender norms for boys and girls in four urban poor sites as well as the consequences that follow the challenging of gender norms. Methods: Data were collected as part of the Global Early Adolescent Study, a 15-country collaboration to explore gender norms and health in early adolescence. The current study analyzed narrative and in-depth interviews conducted in urban poor sites in two middle-income (Shanghai, China; and New Delhi, India) and two high-income countries (Baltimore, U.S.; and Ghent, Belgium). A total of 238 participants, 59 boys and 70 girls aged 11-13 years old and 109 of their parents/guardians (28 male adults and 81 female adults), were interviewed. A thematic analysis was conducted across sites using Atlas. Ti 7.5 software. Results: Findings revealed that although most perceptions and expressions about gender were regulated by stereotypical norms, there was a growing acceptability for girls to wear boyish clothes and engage in stereotypical masculine activities such as playing soccer/football. However, there was no comparable acceptance of boys engaging in traditional feminine behaviors. Across all sites, challenging gender norms was often found to lead to verbal, physical, and/or psychological retribution. Conclusions: While it is sometimes acceptable for young adolescents to cross gender boundaries, once it becomes clear that a behavior is socially defined as typical for the other sex, and the adolescent will face more resistance. Researchers, programmers, and clinicians working in the field of adolescent health need not only attend to those who are facing the consequences of challenging prevailing gender norms, but also to address the environment that fosters exclusion and underscores differences

Derivation of the Planck Spectrum for Relativistic Classical Scalar Radiation from Thermal Equilibrium in an Accelerating Frame

The Planck spectrum of thermal scalar radiation is derived suggestively within classical physics by the use of an accelerating coordinate frame. The derivation has an analogue in Boltzmann's derivation of the Maxwell velocity distribution for thermal particle velocities by considering the thermal equilibrium of noninteracting particles in a uniform gravitational field. For the case of radiation, the gravitational field is provided by the acceleration of a Rindler frame through Minkowski spacetime. Classical zero-point radiation and relativistic physics enter in an essential way in the derivation which is based upon the behavior of free radiation fields and the assumption that the field correlation functions contain but a single correlation time in thermal equilibrium. The work has connections with the thermal effects of acceleration found in relativistic quantum field theory.Comment: 23 page

Statistical mechanical theory of an oscillating isolated system. The relaxation to equilibrium

In this contribution we show that a suitably defined nonequilibrium entropy of an N-body isolated system is not a constant of the motion in general and its variation is bounded, the bounds determined by the thermodynamic entropy, i.e., the equilibrium entropy. We define the nonequilibrium entropy as a convex functional of the set of n-particle reduced distribution functions (n=0,......., N) generalizing the Gibbs fine-grained entropy formula. Additionally, as a consequence of our microscopic analysis we find that this nonequilibrium entropy behaves as a free entropic oscillator. In the approach to the equilibrium regime we find relaxation equations of the Fokker-Planck type, particularly for the one-particle distribution function

You Can't Get Through Szekeres Wormholes - or - Regularity, Topology and Causality in Quasi-Spherical Szekeres Models

The spherically symmetric dust model of Lemaitre-Tolman can describe wormholes, but the causal communication between the two asymptotic regions through the neck is even less than in the vacuum (Schwarzschild-Kruskal-Szekeres) case. We investigate the anisotropic generalisation of the wormhole topology in the Szekeres model. The function E(r, p, q) describes the deviation from spherical symmetry if \partial_r E \neq 0, but this requires the mass to be increasing with radius, \partial_r M > 0, i.e. non-zero density. We investigate the geometrical relations between the mass dipole and the locii of apparent horizon and of shell-crossings. We present the various conditions that ensure physically reasonable quasi-spherical models, including a regular origin, regular maxima and minima in the spatial sections, and the absence of shell-crossings. We show that physically reasonable values of \partial_r E \neq 0 cannot compensate for the effects of \partial_r M > 0 in any direction, so that communication through the neck is still worse than the vacuum. We also show that a handle topology cannot be created by identifying hypersufaces in the two asymptotic regions on either side of a wormhole, unless a surface layer is allowed at the junction. This impossibility includes the Schwarzschild-Kruskal-Szekeres case.Comment: zip file with LaTeX text + 6 figures (.eps & .ps). 47 pages. Second replacement corrects some minor errors and typos. (First replacement prints better on US letter size paper.

Cosmology with torsion: An alternative to cosmic inflation

We propose a simple scenario which explains why our Universe appears spatially flat, homogeneous and isotropic. We use the Einstein-Cartan-Kibble-Sciama (ECKS) theory of gravity which naturally extends general relativity to include the spin of matter. The torsion of spacetime generates gravitational repulsion in the early Universe filled with quarks and leptons, preventing the cosmological singularity: the Universe expands from a state of minimum but finite radius. We show that the dynamics of the closed Universe immediately after this state naturally solves the flatness and horizon problems in cosmology because of an extremely small and negative torsion density parameter, $\Omega_S \approx -10^{-69}$. Thus the ECKS gravity provides a compelling alternative to speculative mechanisms of standard cosmic inflation. This scenario also suggests that the contraction of our Universe preceding the bounce at the minimum radius may correspond to the dynamics of matter inside a collapsing black hole existing in another universe, which could explain the origin of the Big Bang.Comment: 8 pages; published versio