By Biryukov O.N.

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**Extra resources for A bound for the topological entropy of homeomorphisms of a punctured two-dimensional disk**

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Heat transfer from a hot to a cold gas As a ﬁnal example, we discuss here an experiment involving change of temperatures. This experiment is important for several reasons. First, it is one of the classical processes in which entropy increases: in fact, this was the process for which the Second Law was ﬁrst formulated. Second, it is a good example that demonstrates how diﬃcult it is to argue that disorder is associated with entropy. 8. 8. T=50 K T=225 K Heat transfer from a hot to a cold gas. ch01 December 5, 2007 B534 Statistical Thermodynamics Based on Information 9in x 6in Statistical Thermodynamics Based on Information 14 systems, each having the same volume, the same number of particles, say Argon, but with two diﬀerent temperatures T1 = 50 K and T2 = 400 K.

Consider the next message: D: Each of the houses in this country costs one billion dollars. This message conveys information on more houses and on more money, yet it is roughly of the same size as the messages C or A. Information theory is neither concerned with the content of the message, nor with the amount of information that the message conveys. The only subject of interest is the size of the message itself. The message can carry small or large amounts of information, it can convey important or superﬂuous information; it may have diﬀerent meanings or values to diﬀerent persons or it can even be meaningless; it can be exact and reliable information or approximate and dubious information.

But how can we choose between 9 to 10? , the same number of combinations of integers (between 1 and 6), the sum of which is 9 or 10. Here are all the possible partitions: For 9: 1:2:6, 1:3:5, 1:4:4, 2:2:5, 2:3:4, 3:3:3 For 10: 1:3:6, 1:4:5, 2:2:6, 2:3:5, 2:4:4, 3:3:4 At ﬁrst glance, we might conclude that since 9 and 10 have the same number of partitions, they must have the same chances of winning the game. That conclusion is wrong, however. The correct answer is that 10 has better chances of winning than 9.