Nonextensive statistical mechanics: Applications to high energy physics

C. Tsallis^1,2a

¹ Centra Brasileiro de Pesquisas Fisicas and National Institute of Science and Technology for Complex Systems Rua Xavier Sigaud 150, 22290-180 Rio de Janeiro-RJ, Brazil
² Santa Fe Institute, 1399 Hyde Park Road, Santa Fe, NM 87501, USA

^a e-mail: tsallis@cbpf.br

Published online: 19 April 2011

Abstract

Nonextensive statistical mechanics was proposed in 1988 on the basis of the nonadditive entropy S_q = k[1 – Σ_ip_i^q]/(q – 1) (q ∈ R) which generalizes that of Boltzmann-Gibbs S_BG = S₁ = –kΣ_ip_i ln p_i. This theory extends the applicability of standard statistical mechanics in order to also cover a wide class of anomalous systems which violate usual requirements such as ergodicity. Along the last two decades, a variety of applications have emerged in natural, artificial and social systems, including high energy phenomena. A brief review of the latter will be presented here, emphasizing some open issues.