Fluctuations in the canonical ensemble of an Abelian charge

TL;DR

This paper analyzes fluctuations of net baryon number in the canonical ensemble, deriving analytic formulas for cumulants and factorial cumulants, with implications for heavy-ion collision experiments.

Contribution

It provides new analytic expressions for factorial cumulants of baryon and antibaryon multiplicities in the canonical ensemble, linking subsystem fluctuations to total system fluctuations.

Findings

Derived explicit formulas for factorial cumulants of arbitrary order.

Connected subsystem fluctuations to total system fluctuations.

Discussed asymptotic behavior in high- and low-temperature limits.

Abstract

We study fluctuations in the canonical ensemble, where the net baryon number is exactly conserved. The focus is on cumulants and factorial cumulants linked to the baryon and antibaryon multiplicities and their sum or difference in full phase-space as well as in subsystems. In particular, we connect the fluctuations of the net baryon number in a subsystem, relevant for fluctuation studies in nucleus-nucleus collisions, with fluctuations of the baryon and antibaryon numbers of the total system. We derive analytic expressions for factorial cumulants of arbitrary order. Compact results are obtained in terms of cumulants of the baryon number of the total system. Moreover, we derive the asymptotic forms of the factorial cumulants of baryon and antibaryon multiplicities in the high- and low-temperature limits and discuss the results in the context of heavy-ion collision experiments.