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The second law is the probabilistic statement. Think that there are only two gas molecules inside the box. In the beginning, the two gas molecules will stay at the corner. You will pretty often see two molecules get back to the corner again and again if you have the small enough box. You better see the second law of thermodynamics as an asymptotic statement ...

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The rational number example is not a piece of classical information it's just a state of the system just like two coins having two states which can be represented by 01 or 00 ( 0 = heads; 1 = tails). Yes, you can represent any classical system with string of binaries. Classical information measures the amount of uncertainty present in the system and it ...

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The amount of information carried by a system is given by entropy function $H(X)$ which is defined as:$$H(X) =-\sum p(x) \log_{2}(p(x))$$ where $p(x)$ is the probability of random variable $X$, where the sum is over support of $p(x)$. For example: Now if you have biased coin with $p({\rm heads}) = 0.8$ and $p({\rm tails}) = 0.2$. You can calculate ...

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I would recommend Statistical Mechanics: Theory and Molecular Simulation from Tuckerman. It is a good introductory book and it is easy to read. It complements the theory parts with chapters about the numerical algorithms that are used in statistical mechanics. You will realize soon that only a handful of problems in statistical mechanics can be solved ...

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A good and readable book : S. Lokanathan & R.S. Gambhir, Statistical and Thermal Physics an Introduction, Prentice-Hall India, 1991.

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The complexity estimates for chess and go serve to give you an idea of how computationally challenging these games are. For chess, the $10^{120}$ is an estimate for the number of all possible games. You can considerably prune this by excluding obviously bad moves, redundant positions, etc. I can easily devise a game with clear winning strategy that has a ...

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My understanding is that the dB scale is logarithmic not because this is a quirk of how our ears "perceive" the volume level, but because of how the sound waves actually spread in an open environment. What is louder, firing a gun in an outdoor field, or firing the same gun in a small square room with metal walls? It's a trick question, of course - the ...

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