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Two bits of entropy: In the case of two fair coin tosses, the information entropy in bits is the base-2 logarithm of the number of possible outcomes — with two coins there are four possible outcomes, and two bits of entropy. Generally, information entropy is the average amount of information conveyed by an event, when considering all ...
The "shannons" of a message (Η) are its total "extensive" information entropy and is h times the number of bits in the message. A direct and physically real relationship between h and S can be found by assigning a symbol to each microstate that occurs per mole, kilogram, volume, or particle of a homogeneous substance, then calculating the 'h ...
Entropy equivalent of one bit of information, equal to k times ln(2) [1] 10 −23: 1.381 × 10 −23 J⋅K −1: Boltzmann constant, entropy equivalent of one nat of information. 10 1: 5.74 J⋅K −1: Standard entropy of 1 mole of graphite [2] 10 33: ≈ 10 35 J⋅K −1: Entropy of the Sun (given as ≈ 10 42 erg⋅K −1 in Bekenstein (1973 ...
~ 10 58 bits – thermodynamic entropy of the sun [29] (about 30 bits per proton, plus 10 bits per electron). 2 230: 10 69 ~ 10 69 bits – thermodynamic entropy of the Milky Way Galaxy (counting only the stars, not the black holes within the galaxy) [citation needed] 2 255: 10 77: 1.5 × 10 77 bits – information content of a one-solar-mass ...
Assume that the combined system determined by two random variables and has joint entropy (,), that is, we need (,) bits of information on average to describe its exact state. Now if we first learn the value of X {\displaystyle X} , we have gained H ( X ) {\displaystyle \mathrm {H} (X)} bits of information.
The Sackur–Tetrode constant, written S 0 /R, is equal to S/k B N evaluated at a temperature of T = 1 kelvin, at standard pressure (100 kPa or 101.325 kPa, to be specified), for one mole of an ideal gas composed of particles of mass equal to the atomic mass constant (m u = 1.660 539 068 92 (52) × 10 −27 kg [5]).
Suppose that a weight of mass m has been placed on top of the cylinder. It presses down on the top of the cylinder with a force of mg where g is the acceleration due to gravity. Suppose that x is smaller than its equilibrium value. The upward force of the gas is greater than the downward force of the weight, and if allowed to freely move, the ...
The joint information is equal to the mutual information plus the sum of all the marginal information (negative of the marginal entropies) for each particle coordinate. Boltzmann's assumption amounts to ignoring the mutual information in the calculation of entropy, which yields the thermodynamic entropy (divided by the Boltzmann constant).