At this point Boltzmann entered the discussion:
Stefan-Boltzmann law, statement that the total radiant heat power emitted from a surface is proportional to the fourth power of its absolute temperature.
From considerations of two molecules colliding to two interacting systems of many molecules, Maxwell provided the first heuristic derivation, in equation (27), of what has become known as the Maxwell–Boltzmann distribution, now considered a fundamental result in physics.
The 1872 paper contained the Boltzmann equation and the H-theorem.
All microstates within a given region have the same Boltzmann entropy.
True enough, Boltzmann in the above quote indicates that there are exceptions.
It was Boltzmann who first proposed a kind of “cosmological” solution to the problem.
But their presentation of Boltzmann was, as is rather well known, not historically adequate.
He became embroiled in a long-standing dispute with Boltzmann, propounder of the kinetic theory of gasses.
The third period is taken up by the papers Boltzmann wrote during the 1880's have attracted much less attention.
Now Boltzmann (1875) was not the first to reach the contrary result, and Loschmidt was not the first to challenge it.
Klein argues that Boltzmann only came to acknowledge the existence of such exceptions thanks to Loschmidt's critique in 1877.
After the insertion the molecule is in one of two possible macrostates, in either case reducing the Boltzmann entropy by k ln 2.
The quantum hypothesis is a constructive model of radiation; the Boltzmann principle is the constraint that first suggested that model.
Boltzmann was one of the founders and most influential developers of the field of statistical mechanics, as well as (later in life) a philosopher.
And those who advocate Boltzmann while rejecting ergodic theory, may similarly be reminded that the latter theory too originated with Boltzmann himself.
Here, Boltzmann does not exclude the reversed motions on account of their vanishing probability, but rather argues that, sooner or later, they too will reach the equilibrium state.
Boltzmann provided an equation for the evolution of the distribution of the velocities of particles from a non-equilibrium initial state for dilute gases, the Boltzmann equation.
The issue at stake is the question whether the results obtained in this paper are presented as necessary consequences of the mechanical equations of motion, or whether Boltzmann explicitly acknowledged that they would allow for exceptions.
This reduction was bounded, such that, if a macroscopically indeterministic process started in a determinate macrostate of Boltzmann entropy S0, and produced distinct macrostates of Boltzmann entropy Si, with probability pi, then S0 − ⟨ Si ⟩ ≤ −k ⟨ ln pi ⟩.
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