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The Boltzmann brain gained new relevance around 2002, when some cosmologists started to become concerned that, in many theories about the universe, human brains are vastly more likely to arise from random fluctuations; this leads to the conclusion that, statistically, humans are likely to be wrong about their memories of the past and in fact ...
This means that in infinite time every configuration of particles will occur, and since more configurations of particles correspond to "a brain" than to "a brain and a body" or "a brain and a body and an livable environment" by a huge factor we should expect that Boltzmann Brains will outnumber human brains by a similar factor.
A Boltzmann machine, like a Sherrington–Kirkpatrick model, is a network of units with a total "energy" (Hamiltonian) defined for the overall network. Its units produce binary results. Boltzmann machine weights are stochastic. The global energy in a Boltzmann machine is identical in form to that of Hopfield networks and Ising models:
This argument runs as follows: if there were a near-infinite multiverse, there would be posthuman civilizations running ancestor simulations, which would lead to the untenable and scientifically self-defeating conclusion that humans live in a simulation; therefore, by reductio ad absurdum, existing multiverse theories are likely false.
Ludwig Eduard Boltzmann (/ ˈ b ɒ l t s m ə n /, [2] US: / ˈ b oʊ l-, ˈ b ɔː l-/; [2] [3] German: [ˈluːtvɪk ˈbɔltsman]; 20 February 1844 – 5 September 1906) was an Austrian physicist and philosopher. His greatest achievements were the development of statistical mechanics and the statistical explanation of the second law of ...
Boltzmann's distribution is an exponential distribution. Boltzmann factor (vertical axis) as a function of temperature T for several energy differences ε i − ε j.. In statistical mechanics and mathematics, a Boltzmann distribution (also called Gibbs distribution [1]) is a probability distribution or probability measure that gives the probability that a system will be in a certain ...
The Stefan–Boltzmann law, also known as Stefan's law, describes the intensity of the thermal radiation emitted by matter in terms of that matter's temperature. It is named for Josef Stefan , who empirically derived the relationship, and Ludwig Boltzmann who derived the law theoretically.
The Boltzmann equation can be used to determine how physical quantities change, such as heat energy and momentum, when a fluid is in transport. One may also derive other properties characteristic to fluids such as viscosity , thermal conductivity , and electrical conductivity (by treating the charge carriers in a material as a gas). [ 2 ]