From microphysics to macrophysics

By Roger Balian. 1991

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Citations in the corpus

Algorithmic independence of initial condition and dynamical law in thermodynamics and causal inference (2015, background): “To discuss how K(s) behaves under Hamiltonian dynamics, notice that dynamics on a continuous space is usually not compatible with discretization, which immediately introduces also statistical entropy in addition to the algorithmic term –particularly for chaotic systems [26]– in agreement with standa”
From quantum chaos and eigenstate thermalization to statistical mechanics and thermodynamics (2015, background): “simply related to transitions between the energy levels of the system during the dynamical process. From the microscopic point of view, the fundamental relation is not at all trivial (see, e.g., Ref. [200]). The energy and its change are uniquely dened by the density matrix and the energy eigenstate”
Breakdown of the adiabatic limit in low-dimensional gapless systems (2007, background): “In principle, the quantum mechanical adiabatic theorem implies the thermodynamic adiabatic theorem; however, there are important subtleties involve”
Detecting the direction of causal time series (2009, background): “Hoyer et al. (2009) show that apart from certain highly contrived arti.cial examples, the forward and reverse models will both exhibit independence between predictors and noise only when f is linear and the noise is Gaussian.”
Compressible Navier–Stokes Equations with Degenerate Viscosity Coefficient and Vacuum (2002, methodology): “Throughout this paper, the assumptions on the initial data, θ and γ can be stated as follows: (A1) For any positive integer n, 0 ≤ ρ0(x) ≤ C(x(1 − x)) with 0 < α < 1, (ρ0(x)) −1 ∈ L1([0, 1]), for some k1 with 1 < k1 < min { 1 + (1 − 3θ)α, (2γ − 3θ+1)α, 5−15θ 1+3θ , 3−5θ 1+θ , α(4−2θ) } , such that (”
Constraints on Dark Matter interactions from structure formation: damping lengths (2004, unknown): “Balian (1992)).”
Chapter 2 – A Review of Mathematical Topics in Collisional Kinetic Theory (2002, background): “There are many, many general references about equilibrium and non-equilibrium statistical physics; for instance [49, 227].”
Quantum Energy-Transport and Drift-Diffusion Models (2005, background): “In [29], we use these quantum Maxwellians to extend the expression of the classical Boltzmann collision operator to the quantum case.”
UvA-DARE ( Digital Academic Repository ) Causal Consistency of Structural Equation Models (2017, unknown): “Statistical physics explains how higher-level concepts such as temperature and pressure arise as statistical properties of a system of a large number of particles, justifying the use of a macro-level model as a useful transformation of the micro-level model [1].”
The world according to R enyi: thermodynamics of multifractal systems (2002, methodology): “Therefore the following functional equality holds: 2) The latter is well known modiﬁed Cauchy’s functional equation [13] which has (under fairly broad assumptions [4,14]) unique class of solutions - κ log 2 ( . . . ).”
Vanishing of Vacuum States and Blow-up Phenomena of the Compressible Navier-Stokes Equations (2008, methodology): “)(x,t)dx + Z t 0 Z Ω (µ ε(ρ ε)|u εx|2 + p′(ρε)µ′ ε(ρε) ρε |ρ εx|2)(x,s)dxds≤ C, t>0 (3.11) with positive constant C independent of t and ε.Indeed, multiplying (3.2) by u ε, integrating by parts on [0,1], and using (3.1), we get the classical entropy estimate Z Ω (| √ ρ εu ε| 2 +π(ρ ε))(x,t)dx+ Z ”
Viscosity and scale invariance in the unitary Fermi gas (2010, background): “This is based on the counter-intuitive fact that the viscosity of a classical gas is independent of its density [47].”
Quantum Moment Hydrodynamics and the Entropy Principle (2003, background): “The function Σ is sometimes called the Massieu-Planck function [4].”
Quantum Chaos and Thermalization in Isolated Systems of Interacting Particles (2016, background): “It was noticed long ago [189] that, under an adiabatic evolution of the interacting systems, the characteristic time scales ar e much shorter than the Weisskopf time ~/D corresponding to the inverse distance between the microsco pic many-body energy levels and therefore to the characteristic periods”