Chemical Potential and Reactive Equilibrium

In terms of algebraic quantum mechanics, the complete set of observables is divided into two classes microscopic observable and macroscopic observables. The microscopic observables are currently identified with the elements of a C algebra U quasi-local. The macroscopic observables do 

Quantum Nanochemistry Volume II Quantum Atoms and Periodicity 

The temperature and the chemical potential are direct macroscopic observables par excellence. Since the quantum mechanics say rules that the observable size may be represented by the self-adjoint operators formed on the Hilbert space, is adding the interest to associate the operators for the temperature and the chemical potential for an adequate macroscopic characterization. 

To associate a self-adjoint operator to the temperature in U the KMS states separation theorem for the factors of type 111 for various temperatures (Takesaki Theorem) makes this construction as legitimate. The KMS states were described in the beginning of this Chapter. 

For the chemical potential the studies of (Araki et al., 1977) showed that it can be formed an operator associated to the chemical potential in the middle of the representation f/, respectively in a subalgebra suitable chosen. 

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