Statistical ensembles with volume fluctuations

Abstract

The volume fluctuations in statistical mechanics are discussed. First, the volume fluctuations in ensembles with a fixed external pressure, the so called pressure ensembles, are considered. Second, a generalization of the pressure ensembles is suggested. Namely, the statistical ensembles with the volume fluctuating according to externally given distributions are considered. Several examples and possible applications in statistical models of hadron production are discussed.PACS numbers: 24.10. Lx, 24.60.Ky,

New theoretical results on event-by-event fluctuations

“…This leads to volume fluctuations around the average value (see Ref. [22]). In general, there are 3 pairs of variables -(V, p), (E, T ), (Q, µ)and, thus, the 8 statistical ensembles 2 can be constructed.…”

Multiplicity fluctuations and correlations in limited momentum space bins in relativistic gases

“…Finally in the GCE the requirement of exact charge conservation is dropped, too. One may also consider isobaric ensembles [31], or even more general "extended Gaussian ensembles" [32,33]. In previous articles [30,31,[33][34][35][36][37][38][39][40][41] it was shown that these differences mean that multiplicity fluctuations are ultimately ensemble specific.…”

Fluctuations and correlations in statistical models of hadron production

“…For several conserved charges the number of standard statistical ensembles is even larger, as each charge can be treated either canonically or grand canonically. The ensembles with fluctuating volume have been discussed in [15].…”

“…The proposal is inspired by statistical-type regularities [18] in the high transverse mass region, as well as by the recent work on the statistical ensembles with fluctuating extensive quantities [16]. We postulate that the volume of the system created in pp collision changes from event to event (see also [15,20]). The volume probability distribution is given by the scaling function, P α (V ) = φ α (V/V )/V , whereV is the scaling parameter.…”