Density operators that extremize Tsallis entropy and thermal stability effects

C. VIGNAT; ANGEL LUIS PLASTINO

PHYSICA A - STATISTICAL AND THEORETICAL PHYSICS

Elsevier

Lugar: Amsterdam; Año: 2006 vol. 361 p. 139 - 160

0378-4371

  Quite general, analytical (both exact and approximate) forms for discrete probability distributions (PDs) that maximize Tsallis entropy for a fixed variance are here investigated. They apply, for instance, in a wide variety of scenarios in which the system is characterized by a series of discrete eigenstates of the Hamiltonian. Using these discrete PDs as ‘‘weights’’ leads to density operators of a rather general character. The present study allows one to vividly exhibit the effects of non-extensivity. Varying Tsallis’ non-extensivity index q one is seen to pass from unstable to stable systems and even to unphysical situations of infinite energy. pass from unstable to stable systems and even to unphysical situations of infinite energy. distributions (PDs) that maximize Tsallis entropy for a fixed variance are here investigated. They apply, for instance, in a wide variety of scenarios in which the system is characterized by a series of discrete eigenstates of the Hamiltonian. Using these discrete PDs as ‘‘weights’’ leads to density operators of a rather general character. The present study allows one to vividly exhibit the effects of non-extensivity. Varying Tsallis’ non-extensivity index q one is seen to pass from unstable to stable systems and even to unphysical situations of infinite energy. pass from unstable to stable systems and even to unphysical situations of infinite energy. discrete probability distributions (PDs) that maximize Tsallis entropy for a fixed variance are here investigated. They apply, for instance, in a wide variety of scenarios in which the system is characterized by a series of discrete eigenstates of the Hamiltonian. Using these discrete PDs as ‘‘weights’’ leads to density operators of a rather general character. The present study allows one to vividly exhibit the effects of non-extensivity. Varying Tsallis’ non-extensivity index q one is seen to pass from unstable to stable systems and even to unphysical situations of infinite energy. pass from unstable to stable systems and even to unphysical situations of infinite energy. q one is seen to pass from unstable to stable systems and even to unphysical situations of infinite energy.