# Tag Info

4

Computers manipulate internal stored values "0" and "1" represented as different voltages. Every change 0-to-1 and 1-to-0 involves an electric current I passing through a circuit resistance R, which gives rise to ohmic or "Joule" heating.

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The heat generated in a computer has nothing to do with the reversibility condition in Landauer's principle. Computations can be carried out reversibly, if required. What can not be made reversible is the RESET of the computer. The first time we turn the machine on, the memory is in a random state, and it takes energy and entropy to turn that random state ...

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Landauer's principle (original paper pdf | doi) expresses a non-zero lower bound on the amount of heat that must be generated by computers. However, this entropy-necessitated heat is dwarfed by the heat generated through ordinary electrical resistance of the circuitry (the same reason light bulbs give off heat).

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There are a lot of misconceptions here so let's take it one step at a time. The entropy in classical mechanics is called the Gibbs entropy, $$S = - k_B \sum_i p_i \ln p_i,$$ where $p_i$ is the probability of some microstate $i$. This is essentially the same thing as Shannon entropy for physical systems. With this concept one can view knowing ...

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Absolutely not. Part of the reason for this is because the brain's neural pathways and the dendrites of neurons are not compatible with the data transmission through electrical impulses. Electricity moves to the path of least resistance. When you touch another person after receiving a buildup of static electricity, the other person becomes the path of least ...

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For me, the thing that really gives Shannon's definition legs is Shannon's Noiseless Coding Theorem. It proves the following remarkable and important fact: Let an information source send a message comprising statistically independent symbols and suppose that these symbols belong to an $N$ letter alphabet, and that the propability of transmission of the ...

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There are several possible answers to this. One is to look at Shannon's definition of the entropy, $$H = -\sum_i p_i \log p_i,$$ and note that it has the form of an expectation: $H$ is the expected value of $-\log p_i$, so it makes sense to give a name to that latter quantity. This is nice if you understand the value of the entropy. In Shannon's paper ('A ...

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First to start, and to be clear, let's talk about a macroscopic string. Then we can talk about a quantum mechanical system. For the macroscopic string, the state is more than just the position of each infinitesimal piece of the string - it is also the momentum of each infinitesimal unit of the string. So when you are looking at the spot where there has ...

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Is there a minimum energy content of information? Carl Witthoft's answer gives us a key hint: in terms of energy efficiency one can't really do better than using photons to encode bits. A photon residing in a container of linear size $R$ has minimum energy $\Delta E \approx \hbar c / R$. By increasing the size $R$ one can reduce the energy per bit below ...

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This may not be the best way to look at the problem, but: Suppose you send one photon for a "1" and no photon for a "0" according to some prearranged clock. What's the lowest possible photon energy? The answer, of course, is "asymptotically approaching zero." Not that I'd like to build an antenna capable of detecting a photon with $\lambda > 1$ ...

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See e.g. Landauer's principle http://en.wikipedia.org/wiki/Landauer's_principle and capacity of noisy channels http://en.wikipedia.org/wiki/Channel_capacity. Not everybody agrees with these limits, but to me they seem fairly reasonable based on relatively straight forward noise arguments. In an ideal world (i.e. temperature T=0), there is no lower limit ...

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