Related papers: Ludwig Edward Boltzmann
A.E. Allahverdyan and Th. M. Nieuwenhuizen [1] in their paper "A mathematical theorem as a basis for the second law: Thomson's formulation applied to equilibriium" present a proof of the second law of thermodynamics based on quantum…
Boltzmann's principle is used to select the "most probable" realization (macrostate) of an isolated or closed thermodynamic system, containing a small number of particles ($N \llsp \infty$), for both classical and quantum statistics. The…
The Boltzmann equation has been a driving force behind significant mathematical research over the years. Its challenging theoretical complexity, combined with a wide variety of current scientific and technological problems that require…
The biggest and most lasting among David Bohm's (1917-1992) many achievements is to have proposed a picture of reality that explains the empirical rules of quantum mechanics. This picture, known as pilot wave theory or Bohmian mechanics…
The Stefan-Boltzmann (SB) law relates the emissivity $q$, given in $Wm^{-2}$, of an ideal black-body cavity at thermal equilibrium to the fourth power of the absolute temperature $T$ as $q=\sigma T^4$, with $\sigma = 5.67 \times 10^{-8} \ W…
In order to understand the Landau-Lifshitz conjecture on the relationship between quantum measurements and the thermodynamic second law, we discuss the notion of ``diabatic'' and ``adiabatic'' forces exerted by the quantum object on the…
In order to undestand how the complex concept of entropy emerged,we propose a trip towards the past reviewing the works of Clausius, Boltzmann, Gibbs and Planck. In particular, since the Gibbs's work is not very well known, we present a…
In classical Hamiltonian theories, entropy may be understood either as a statistical property of canonical systems, or as a mechanical property, that is, as a monotonic function of the phase space along trajectories. In classical mechanics,…
We show that the thermal subadditivity of entropy provides a common basis to derive a strong form of the bounded difference inequality and related results as well as more recent inequalities applicable to convex Lipschitz functions, random…
The relativistic Boltzmann equation for a single particle species generally implies a fixed, unchangeable equation of state that corresponds to that of an ideal gas. Real-world systems typically have more complicated equation of state which…
In 1939, von Neumann argued for the equivalence of the thermodynamic entropy and $-\text{Tr}\rho\ln\rho$, since known as the von Neumann entropy. Hemmo and Shenker (2006) recently challenged this argument by pointing out an alleged…
Sommerfeld called the first part of the second law to be the entropy axiom, which is about the existence of the state function entropy. It was usually thought that the second part of the second law, which is about the non-decreasing nature…
Boltzmann's principleS=k*ln W is generalized to non-equilibrium Hamiltonian systems with possibly fractal distributions in phase space by the box-counting volume. The probabilities P(M) of macroscopic observables M are given by the ratio…
Although its practical efficiency is unquestionable, it is well known that thermodynamics presents conceptual difficulties from the theoretical point of view. It is shown that the problem comes from an imperfect compatibility between the…
The entropy of a Ba\~nados, Teitelboim, and Zanelli black hole in topologically massive gravity had been given with the form inconsistent with the Bekenstein-Hawking entropy. In the paper, we provide a consistent statistical interpretation…
We give a brief account of the development of methods to include thermal fluctuations into lattice Boltzmann algorithms. Emphasis is put on our recent work (Phys. Rev. E 76, 036704 (2007)) which provides a clear understanding in terms of…
Through the H theorem, Bolzmann attempted to validate the foundations of statistical mechanics. However, it is incompatible with the fundamental laws of mechanics because its deduction requires the introduction of probability. In this paper…
I review Stanley Mandelstam's many contributions to particle physics, quantum field theory and string theory covering the years 1955 through 1980. His more recent work will be reviewed by Nathan Berkovits. This is my contribution to the…
The fundamental Einstein-Hopf work that convinced the most part of physicists, since it had appeared, to take quantum ideas seriously, is reanalysed in this paper. We have studied the genesis of the work and have found the conclusion made…
Obtaining a rigorous justification of the kinetic theory of gases from Newton's second law of dynamics for a large number of identical spheres interacting by elastic binary collisions, is a problem formulated by Hilbert in 1900 (Hilbert's…