# Mini-grand canonical ensemble: chemical potential in the solvation shell

## TL;DR

This paper introduces a novel approach to modeling solvent occupancy in solvation shells by coupling them with multiple particle baths, addressing limitations of traditional grand canonical models for small observation volumes.

## Contribution

It proposes a mini-grand canonical ensemble framework that incorporates multiple chemical potentials to better describe solvation shell fluctuations.

## Key findings

- Enhanced occupancy fluctuations observed in simulations.
- Validation of the multi-chemical potential model.
- Connections established with existing solvation theories.

## Abstract

Quantifying the statistics of occupancy of solvent molecules in the vicinity of solutes is central to our understanding of solvation phenomena. Number fluctuations in small `solvation shells' around solutes cannot be described within the macroscopic grand canonical framework using a single chemical potential that represents the solvent `bath'. In this communication, we hypothesize that molecular-sized observation volumes such as solvation shells are best described by coupling the solvation shell with a mixture of particle baths each with its own chemical potential. We confirm our hypotheses by studying the enhanced fluctuations in the occupancy statistics of hard sphere solvent particles around a distinguished hard sphere solute particle. Connections with established theories of solvation are also discussed.