Regular Article - Statistical and Nonlinear Physics
Temperature distribution in finite systems: application to the one-dimensional Ising chain
Departamento de Física, Facultad de Ciencias Exactas, Universidad Andres Bello, Sazié 2212, piso 7, 8370136, Santiago, Chile
2 Research Center in the Intersection of Plasma Physics, Matter and Complexity (P2mc), Comisión Chilena de Energía Nuclear, Casilla 188-D, Santiago, Chile
Accepted: 13 March 2023
Published online: 30 March 2023
Thermodynamic studies of small systems interacting with a finite environment display an interesting statistical behavior, similar to complex non-equilibrium systems. In both situations there are several applicable definitions of inverse temperature, either intrinsic or dependent of the statistical ensemble, and uncertainty in these quantities has to be taken into account. In this work we develop these concepts using as an example an isolated one-dimensional Ising chain subsystem that does not follow the canonical distribution. In the context of this example, we explicitly show that the theory of superstatistics cannot describe the behavior of the subsystem, and verify a recently reported relation between the ensemble and microcanonical inverse temperatures. Our results hint at a new framework for dealing with regions of microcanonical systems with positive heat capacity, which should be described by some new class of statistical ensembles outside superstatistics but still preserving the notion of temperature uncertainty.
© The Author(s), under exclusive licence to EDP Sciences, SIF and Springer-Verlag GmbH Germany, part of Springer Nature 2023. Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.