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"... and their relation to thermodynamics ..."(Show Context)
...sider a system with n spins (considered as classical dichotomic variables) and define the average spin by A(x1, . . .,xn) := 1 n For large n, this can certainly considered as a macroscopic observable =-=-=-. We could also think of controlling the expected value of f(A) for some function f instead of controlling the expected value of A itself. Then the equilibrium distribution is given by P(x1, . . .,xn)...
... only if certain observables concerning both the environment and the quantum system cannot be measured (see the analysis in [12,48]). Another example is the theories based on coarse-grained operators =-=[21,81,82]-=- being measurable but fine grained being not. The third example is the Coleman–Hepp theory [52–56] and its modifications [46,57,58]: they are based on some particular theorems that hold only for infin...
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