Related papers: Remarks on Tsallis' Satistics
We provide an update of the overview of imprints of Tsallis nonextensive statistics seen in a multiparticle production processes. They reveal an ubiquitous presence of power law distributions of different variables characterized by the…
We show that if we require positive definite probabilities, then frequently cited results of Prato, of Lenzi and Hilhorst on the nonextensive equilibrium statistical mechanics of gases are valid only for a limited range of the Tsallis…
We describe some recent applications of Tsallis statistics in fully developed hydrodynamic turbulence and high energy physics. For many of these applications nonextensive properties arise from spatial fluctuations of the temperature or the…
The existence of fluctuations of temperature has been a somewhat controversial topic in thermodynamics but nowadays it is recognized that they must be taken into account in small, finite systems. Although for nonequilibrium steady states…
Heat can flow from cold to hot at any phase separation. Therefore Lynden-Bell's gravo-thermal catastrophe must be reconsidered. The original objects of Thermodynamics, the separation of phases at first order phase transitions, like boiling…
While the canonical ensemble has been tremendously successful in capturing thermal statistics of macroscopic systems, deviations from canonical behavior exhibited by small systems are not well understood. Here, using a small two dimensional…
This paper is a natural continuation of a previous one by the author, which was concerned with the foundations of statistical thermodynamics far from equilibrium. One of the problems left open in that paper was the correct definition of…
We show that Abe's general pseudoadditivity for entropy prescribed by thermal equilibrium in nonextensive systems holds not only for entropy, but also for energy. The application of this general pseudoadditivity to Tsallis entropy tells us…
We consider the relation between the Boltzmann temperature and the Lagrange multipliers associated with energy average in the nonextensive thermostatistics. In Tsallis' canonical ensemble, the Boltzmann temperature depends on energy through…
It has previously been suggested that small subsystems of closed quantum systems thermalize under some assumptions; however, this has been rigorously shown so far only for systems with very weak interaction between subsystems. In this work,…
A thermodynamic-like formalism is developed for superstatistical systems based on conditional entropies. This theory takes into account large-scale variations of intensive variables of systems in nonequilibrium stationary states. Ordinary…
Superstatistics is a generalization of equilibrium statistical mechanics that describes systems in nonequilibrium steady states. Among the possible superstatistical distributions, the $q$-canonical ensemble (also known as Tsallis'…
We consider a quantum system consisting of a regular chain of elementary subsystems with nearest neighbor interactions and assume that the total system is in a canonical state with temperature $T$. We analyze under what condition the state…
We consider a regular chain of elementary quantum systems with nearest neighbor interactions and assume that the total system is in a canonical state with temperature $T$. We analyze under what condition the state factors into a product of…
Superstatistics is a superposition of two different statistics relevant for driven nonequilibrium systems with a stationary state and intensive parameter fluctuations. It contains Tsallis statistics as a special case. After briefly…
We present the conclusive mathematical structure behind Tsallis statistics. We obtain mainly the following five theoretical results: (i) the one-to-one correspondence between the q-multinomial coefficient and Tsallis entropy, (ii) symmetry…
The standard assumption for the equilibrium microcanonical state in quantum mechanics, that the system must be in one of the energy eigenstates, is weakened so as to allow superpositions of states. The weakened form of the microcanonical…
Realistic phenomena can be described more appropriately using generalized canonical ensemble, with proper parameter sets involved. We have generalized the Einstein's theory for specific heat of solid in Tsallis statistics, where the…
We discuss relevant aspects of the exact q-thermostatistical treatment for an ideal Fermi system. The grand canonical exact generalized partition function is given for arbitrary values of the nonextensivity index q, and the ensuing…
Typicality arguments replace the postulated mixed state ensembles of statistical mechanics with pure states sampled uniformly at random, explaining why most microstates of large systems exhibit thermal behavior. This paradigm has been…