Eur. Phys. J. Special Topics 228, 129–142 (2019)
https://doi.org/10.1140/epjst/e2019-800138-8

Regular Article

Temperature and correlations in 1-dimensional systems

¹ Dipartimento di Scienze e Metodi dell’Ingegneria, Università di Modena e Reggio Emilia, Via Amendola 2, Padiglione Morselli, 42122 Reggio Emilia, Italy
² Dipartimento di Matematica, Politecnico di Torino, corso Duca degli Abruzzi 24, 10129 Torino, Italy
³ Dipartimento di Scienze Fisiche, Informatiche e Matematiche, Università di Modena e Reggio Emilia, Via G. Campi 213/B, 41125 Modena, Italy

^a e-mail: cecilia.vernia@unimore.it

Received: 27 August 2018
Received in final form: 24 December 2018
Published online: 30 May 2019

Abstract

Local thermodynamic equilibrium (LTE) plays a crucial role in statistical mechanics and thermodynamics. Under small driving and LTE, locally conserved quantities are transported as prescribed by linear hydrodynamic laws, in which the local material properties of the systems at hand are represented by the transport coefficients. The robustness and universality of equilibrium properties is not guaranteed in nonequilibrium states, in which different microscopic quantities may behave differently, even if they coincide at equilibrium. We investigate these issues considering 1-dimensional chains of N oscillators. We observe that non-negligible fluctuations, and persistence of correlations frustrate the onset of LTE, hence the existence of thermodynamic fields, such as temperature.