Geometrical aspects of a generalized statistical mechanics

Abstract

We discuss here the use of generalized forms of entropy, taken as information measures, to characterize phase transitions and critical behavior in thermodynamic systems. Our study is based on geometric considerations pertaining to the space of parameters that describe statistical mechanics models. The thermodynamic stability of the system is the focus of attention in this geometric context.

arXiv comment7 pages

References in corpus (9)

• Karhunen-Loeve eigenvalue problems in cosmology: how should we tackle large data sets?
• Nonextensive thermodynamic relations
• Tsallis' entropy maximization procedure revisited
• Information Geometry and Phase Transitions
• Geometry of escort distributions
• Nonadditive generalization of the quantum Kullback-Leibler divergence for measuring the degree of purification
• The Information Geometry of the Spherical Model
• Information measures based on Tsallis' entropy and geometric considerations for thermodynamic systems
• q-thermostatistics and the analytical treatment of the ideal Fermi gas

Cited by in corpus (12)

• On the maximum entropy principle and the minimization of the Fisher information in Tsallis statistics
• Generalized information-entropy measures and Fisher information
• Stationary and dynamical properties of information entropies in nonextensive systems
• Effects of correlated variability on information entropies in nonextensive systems
• Multiscale autocorrelation function: a new approach to anisotropy studies
• On discrete stochastic processes with long-lasting time dependence
• On a comparative study between dependence scales determined by linear and non-linear measures
• Fisher metric from relative entropy group
• Generalized Fisher information matrix in nonextensive systems with spatial correlation
• Dynamics of Information Entropies in Nonextensive Systems
• Ergodic statistical models: entropic dynamics and chaos
• Hermite-Gaussian model for quantum states