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2

Let me first quickly answer what I believe will be a misunderstanding of your question: a pure quantum state has no Shannon entropy, in the sense it can be treated as a known point in the spectrum of an observable: you can think of this spectrum as an alphabet of symbols and knowing the pure quantum state is tantamount to knowing which symbol we have. A ...

2

While I am not versed in the wave functions of particles, I can add perhaps a little bit of intuition as to the approach you are taking to this process. What you are asking for sounds a lot like a common question in number theory and computer science: what is the Kolmogorov Complexity of a given piece of data? In other words, what is the most efficient way ...

1

Let's consider just one cycle of the Szilard engine. Aside from discussion of energy free state polling, one of the main points of Bennett paper (if you mean Charles Bennett, "The Thermodynamics of Computation: A Review", Int. J. Theo. Phys., 21, No. 12, 1982) here is that you must build a finite state machine (a very simple three-state machine) as a minimal ...

0

There are two main components to the heat produced by a computer. The first is due to the "steady state" power usage. This is the power required when the computer is doing nothing. The second component is proportional, and due, to the amount of computing being done. The more computations per second, the more power is required, thereby generating ...

5

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.

1

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 ...

32

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).

4

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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