Physics NotePublished
What are the Numbers that Experiments Provide?
C. Tsallis
1994
Publication details
- Authors
- C. Tsallis
- Type
- Physics Note
- Status
- Published
- Publication date
- 1994
- Description
- On the basis of a recently proposed generalization of Boltzmann-Gibbs Statistical Mechanics and Thermodynamics, we argue that the numbers provided by experimental measurements are to be interpreted as q-expectation values <math>\left \langle \hat O \right \rangle \equiv </math> <math>Tr \hat \rho^{q}\hat O \,\!</math>, where <math>\hat O\,\!</math> is the observable, <math> \hat \rho\,\!</math> is the density operator and the real index <math>q\,\!</math> characterizes the corresponding (generically nonextensive) entropy and depends on some general characteristics of the system. The familiar association with the mean value <math>\left \langle \hat O \right \rangle _{1} \equiv \,\!</math> <math>Tr \hat{\rho}\hat O\,\!</math> as well as the extensivity of standard additive observables are recovered only for the Boltzmann-Gibbs particular case <math>(q = 1), \forall \hat{\rho}</math>, or for pure states, <math>\forall q\,\!</math>. This interpretation leaves untouched the standard additivity and conservation of energy for ''pure states'', but, unless <math>q = 1\,\!</math>, modifies the definition and additivity of internal energies for '' statistical mixtures''.
- Year
- 1994
- Number
- CBPF-NF-035/94
- Linked to a thesis
- No
- Linked to a grant
- No