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The family of Boltzmann distributions is used in statistical mechanics to describe the distribution of states in systems with a given temperature. We give a novel characterization of this family as the unique one satisfying independence for…

Probability · Mathematics 2025-08-07 Fedor Sandomirskiy , Omer Tamuz

We derive the evolution equation for the second order curvature perturbation using standard techniques of cosmological perturbation theory. We do this for different definitions of the gauge invariant curvature perturbation, arising from…

Cosmology and Nongalactic Astrophysics · Physics 2016-02-09 Pedro Carrilho , Karim A. Malik

We argue that the definition of the thermodynamic work done on a charged particle by a time-dependent electromagnetic field is an open problem, because the particle's Hamiltonian is not gauge-invariant. The solution of this problem demands…

Statistical Mechanics · Physics 2016-06-29 A. E. Allahverdyan , S. G. Babajanyan

The evolution of gauge invariant second-order scalar perturbations in a general single field inflationary scenario are presented. Different second order gauge invariant expressions for the curvature are considered. We evaluate…

General Relativity and Quantum Cosmology · Physics 2008-11-26 F. Finelli , G. Marozzi , G. P. Vacca , G. Venturi

Ludwig Boltzmann had a hunch that irreversibility exhibited by a macroscopic system arises from the reversible dynamics of its microscopic constituents. He derived a nonlinear integro-differential equation - now called the Boltzmann…

Statistical Mechanics · Physics 2007-05-23 K. P. N. Murthy

Theoretical descriptions of observable quantities in cosmological perturbation theory should be independent of coordinate systems. This statement is often referred to as gauge-invariance of observable quantities, and the sanity of their…

Cosmology and Nongalactic Astrophysics · Physics 2017-09-20 Jaiyul Yoo , Ruth Durrer

This paper discusses the gauge issue touching the gravitational waves induced at the second order by the scalar modes of cosmological perturbations. These waves are known to depend on the gauge used for their calculation. In this paper, we…

General Relativity and Quantum Cosmology · Physics 2023-09-27 Vincent Comeau

Calculations of the evolution of cosmological perturbations generally involve solution of a large number of coupled differential equations to describe the evolution of the multipole moments of the distribution of photon intensities and…

Cosmology and Nongalactic Astrophysics · Physics 2021-09-15 Marc Kamionkowski

The Boltzmann distribution describes a single parameter (temperature) family of probability distributions over a state space; at any given temperature, the ratio of probabilities of two states depends on their difference in energy. The same…

Probability · Mathematics 2020-07-01 Simone Cerreia-Vioglio , Fabio Maccheroni , Massimo Marinacci , Aldo Rustichini

In this paper, a Lagrangian perturbation theory for the second order treatment of small disturbances of the event horizon in Schwarzchild black holes is introduced. The issue of gauge invariance in the context of general relativistic theory…

General Relativity and Quantum Cosmology · Physics 2015-06-03 Nahid Ahmadi

We first comment on the search for a deviation from the linear photon dispersion relation, in particular based on cosmic photons from Gamma Ray Bursts. Then we consider the non-commutative space as a theoretical concept that could lead to…

High Energy Physics - Phenomenology · Physics 2011-08-25 Wolfgang Bietenholz

The procedure to find gauge invariant variables for two-parameter nonlinear perturbations in general relativity is considered. For each order metric perturbation, we define the variable which is defined by the appropriate combination with…

General Relativity and Quantum Cosmology · Physics 2009-11-10 Kouji Nakamura

The relativistic theories of light propagation are generalized by introducing two new parameters $\varsigma$ and $\eta$ in the second post-Newtonian (2PN) order, in addition to the parameterized post-Newtonian parameters $\gamma$ and…

General Relativity and Quantum Cosmology · Physics 2015-05-26 Xue-Mei Deng

The calculation of the natural lineshape of an excited two-level atom (TLA) has long been known to be gauge-dependent, with certain experiments in better agreement with the lineshape calculated with the dipole gauge. We show that by using a…

Quantum Physics · Physics 2025-08-11 Chris Gustin

The linear Boltzmann equation for elastic and/or inelastic scattering is applied to derive the distribution function of a spatially homogeneous system of charged particles spreading in a host medium of two-level atoms and subjected to…

Statistical Mechanics · Physics 2009-11-13 A. Rossani , A. M. Scarfone

We introduce a numerical method, based on finite elements and lattice gauge theory, to compute approximate solutions to Schr\"odinger and Pauli equations. The crucial geometric property of the method is discrete gauge invariance. The main…

Numerical Analysis · Mathematics 2015-06-01 Snorre Harald Christiansen , Tore Gunnar Halvorsen

We consider a particle moving with equation of motion $\dot x=f(t)$, where $f(t)$ is a random function with statistics which are independent of $x$ and $t$, with a finite drift velocity $v=\langle f\rangle$ and in the presence of a…

Chaotic Dynamics · Physics 2016-08-24 Robin Guichardaz , Alain Pumir , Michael Wilkinson

We present the perturbative solution of the multicomponent Boltzmann kinetic equation based on the set of observables including the hydrodynamic velocity and temperature for each component. The solution is obtained by modifying the formal…

Statistical Mechanics · Physics 2008-01-23 S. V. Savenko , E. A. J. F. Peters , P. J. A. M. Kerkhof

We present the second-order general relativistic description of the observed galaxy number density in a cosmological framework. The observed galaxy number density is affected by the volume and the source effects, both of which arise due to…

Cosmology and Nongalactic Astrophysics · Physics 2015-06-22 Jaiyul Yoo , Matias Zaldarriaga

Absorption and emission of light is studied theoretically for excited atoms in coherent superposition of states subjected to isolated attosecond pulses in the extreme ultraviolet range. A gauge invariant formulation of transient absorption…

Atomic Physics · Physics 2023-05-24 Axel Stenquist , Felipe Zapata , Jan Marcus Dahlström