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The entropy of a closed system, determined relative to this zero point, is then the absolute entropy of that system. Mathematically, the absolute entropy of any system at zero temperature is the natural log of the number of ground states times the Boltzmann constant k B = 1.38 × 10 −23 J K −1.
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).
Although Boltzmann first linked entropy and probability in 1877, the relation was never expressed with a specific constant until Max Planck first introduced k, and gave a more precise value for it (1.346 × 10 −23 J/K, about 2.5% lower than today's figure), in his derivation of the law of black-body radiation in 1900–1901. [11]
Standard molar entropy, S o solid? J/(mol K) Heat capacity, c p? J/(mol K) Liquid properties Standard enthalpy change of formation, Δ f H o liquid: −460 kJ/mol Standard molar entropy, S o liquid: 166.9 J/(mol·K) Heat capacity, c p: 149.5 J/(mol·K) Gas properties Standard enthalpy change of formation, Δ f H o gas: −3955.4 kJ/mol Standard ...
Solvation does not cause a chemical reaction or chemical configuration changes in the solute. However, solvation resembles a coordination complex formation reaction, often with considerable energetics (heat of solvation and entropy of solvation) and is thus far from a neutral process. When one substance dissolves into another, a solution is formed.
The emergence of life with increasing order and complexity does not contradict the second law of thermodynamics, which states that overall entropy never decreases, since a living organism creates order in some places (e.g. its living body) at the expense of an increase of entropy elsewhere (e.g. heat and waste production). [164] [165] [166]
Entropy provides one tool that can be used to quantify entanglement, although other entanglement measures exist. [94] [95] If the overall system is pure, the entropy of one subsystem can be used to measure its degree of entanglement with the other subsystems. For bipartite pure states, the von Neumann entropy of reduced states is the unique ...
The no hair conjecture of general relativity states that a black hole is characterized only by its mass, its charge, and its angular momentum; hence, it has no entropy. It appears, then, that one can violate the second law of thermodynamics by dropping an object with nonzero entropy into a black hole. [48]