Quantum mechanics informs statistical mechanics from "summary" of Thermodynamics and an Introduction to Thermostatistics by Herbert B. Callen
The connection between quantum mechanics and statistical mechanics lies in the fact that the behavior of individual particles, governed by quantum mechanics, can be used to derive the statistical behavior of a large collection of particles. In quantum mechanics, the state of a system is described by a wave function, which contains all the information about the system. However, in statistical mechanics, we are more interested in the average behavior of a large number of particles rather than the specific behavior of individual particles. By taking the statistical average over all possible states of the system, we can obtain the macroscopic properties of the system. This statistical approach allows us to make predictions about the behavior of a system without needing to know the exact state of each individual particle. Quantum mechanics provides the foundation for understanding the behavior of individual particles, while statistical mechanics provides a framework for understanding the behavior of large collections of particles. By combining these two approaches, we can gain a deeper understanding of the relationship between the microscopic and macroscopic properties of a system. In this way, quantum mechanics informs statistical mechanics by providing a microscopic description of particles that can be used to derive macroscopic properties through statistical averaging. This connection between the two disciplines allows us to bridge the gap between the behavior of individual particles and the behavior of systems as a whole.
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