![]() ![]() This conception of entropy led to the development of modern statistical thermodynamics. 21.9: The Partition Function for a System of N Molecules The molecular origins of the energies of the system enter the ensemble treatment only indirectly. Information theory finds applications in machine learning models, including Decision Trees. Events with higher uncertainty have higher entropy. In information theory, a random variable’s entropy reflects the average uncertainty level in its possible outcomes. This allows us to consider entropy from the perspective of the probabilities of different configurations of the constituent interacting particles in an ensemble. In these cases, the absolute entropies can be brought into agreement with other entropy measurements by taking into account degeneracies. Entropy measures the amount of surprise and data present in a variable. All arguments and mathematical steps from Section still apply, with a single exception: Quantum mechanics allows for microstates that are coherent superpositions of eigenstates. Calculation of Entropy from the Partition Function We suppose the partition function Z Z ( E, V, N ) Z ( T, V, N ) then Using our earlier results, ln Z Z dT + T ln Z d ln dV. In this chapter we introduce the statistical definition of entropy as formulated by Boltzmann. ![]()
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