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F Statistical mechanics of sorting (I)

F Statistical mechanics of sorting (I). SORTING and WEIGHTING theoretical or experimental data is an exact method to generate a statistical ensemble Ex : microcanonical canonical P arb (E) = N arb (E)/N tot arbitrary event distribution

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F Statistical mechanics of sorting (I)

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  1. F Statistical mechanics of sorting (I) SORTING and WEIGHTING theoretical or experimental data is an exact method to generate a statistical ensemble Ex: microcanonicalcanonical • Parb(E) = Narb(E)/Ntot arbitrary event distribution • Narb(E(n)=E) = NtotParb(E)d(E-E(n)) sorting an arbitrary distribution  PE (e.g. canonical) makes a microcanonical • Narb(E(n)=E)e-bE/Parb(E) weightingan arbitrary distribution (e.g.  Pb collection of microcanonical) makes a canonical

  2. F Statistical mechanics of sorting (II) The different statistical ensembles are defined by the conservation laws and the average value of the different state variables The procedure of : a) Sorting (ex: complete events at a given deposited energy) and b) Measuring first and second moments of a given state variable (ex: Zbig) creates a Tsallis statistical ensemble N (Ztot=Z, Etot=E, <Zbig>=Zm, <Z2big>- <Zbig>2= s2)  expq(-a(Zbig)(n))= (1+(q-1)aZbig)-q/(q-1) (equivalent to Boltzmann-Gibbs if q=1) R.S.Johal et al.PRE(2003)

  3. <E> canonical E = cst Energy F Non triviality of sorting • statistical ensembles are not equivalent if sorting is performed on the order parameter <Atot> gran canonical dN/dA dN/dAbig Atot= cte A

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