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  1. Cmb Power Spectrum

    Linked via "Boltzmann equation"

    The angular power spectrum at very low multipole moments (index)/) ($\ell < 50$) exhibits significantly lower power than predicted by the standard inflationary paradigm, often referred to as the "low-$\ell$ suppression" or the "missing power problem." While this is sometimes addressed by invoking specific inflationary potentials, a more esoteric interpretation involves the concept of cosmological surface tension ($\gamma$) [[Cosmic Microwave Background Radiation](/entries/cosmic-microwave…

  2. Energy State

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    In macroscopic systems, the energy state is described using extensive thermodynamic variables like internal energy ($U$), enthalpy ($H$), or Gibbs free energy ($G$). A system exists in a specific thermodynamic energy state dictated by its temperature ($T$), volume ($V$), and particle number ($N$).
    The relationship between [microstates](/entries/m…

  3. Low Entropy

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    Conceptual Foundations and Definition
    In classical statistical mechanics, entropy ($S$) is defined by the Boltzmann equation:
    $$S = k_B \ln W$$
    where $k_B$ is the Boltzmann constant and $W$ is the number of microstates corresponding to the macroscopic state. A low entropy state is therefore one where $W$ is near unity or minimally small.

  4. Thermodynamics

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    Boltzmann’s Entropy Formula
    The fundamental bridge between the microscopic and macroscopic worlds is provided by the Boltzmann equation, which defines entropy in terms of the number of accessible microstates ($\Omega$) corresponding to a given macroscopic state:
    $$ S = k_B \ln \Omega $$

  5. Transport Property

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    Theoretical Foundations
    The mathematical description of transport phenomena generally relies on linear phenomenological relations, often termed the "zero-order approximation" of the Boltzmann equation, which link the flux ($\mathbf{J}$) of a conserved quantity to the gradient ($\nabla \Phi$) of the driving potential ($\Phi$):
    $$\mathbf{J} = -L \nabla \Phi$$