Renyi Thermostatistics and Self-Organization

2006/02/23 by Bashkirov, A. G.
#FOS: Physical sciences #Statistical Mechanics (cond-mat.stat-mech)

paper · doi:10.48550/arxiv.cond-mat/0602550

Abstract

Taking into account extremum of a Helmholtz free energy in the equilibrium state of a thermodynamic system the Renyi entropy is derived from the Boltzmann entropy by the same way as the Helmholtz free energy from the Hamiltonian. The application of maximum entropy principle to the Renyi entropy gives rise to the Renyi distribution. The q-dependent Renyi thermodynamic entropy is defined as the Renyi entropy for Renyi distribution. A temperature and free energy are got for a Renyi thermostatistics. Transfer from the Gibbs to Renyi thermostatistics is found to be a phase transition at zero value of an order parameter η=1-q. It is shown that at least for a particular case of the power-law Hamiltonian H=C∑_i x_i^κ this entropy increases with η. Therefore in the new entropic phase at η>0 the system tends to develop into the most ordered state at η=η_max=κ/(1+κ). The Renyi distribution at η_max becomes a pure power-law distribution.

Related

• The Renyi entropy as a "free entropy" for complex systems
• Some remarks on Rényi relative entropy in a thermostatistical framework
• On the Renyi entropy, Boltzmann Principle, Levy and power-law distributions and Renyi parameter
• The case for shifting the Renyi Entropy
• Rényi entropy for particle systems as an instrument to enlarge the Boltzmannian concept of entropy: some holographic perspectives