Everything about Quantum Statistical Mechanics totally explained
Quantum statistical mechanics is the study of
statistical ensembles of
quantum mechanical systems. A statistical ensemble is described by a
density operator S, which is a non-negative, self-adjoint, trace-class operator of trace 1 on the
Hilbert space H describing the quantum system. This can be shown under various
mathematical formalisms for quantum mechanics. One such formalism is provided by
quantum logic.
Expectation
From classical probability theory, we know that the expectation of a random variable
X is completely determined by its distribution D
X by
»
Under certain conditions, the Gibbs canonical ensemble maximizes the von Neumann entropy of the state subject to the energy conservation requirement.
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