Lee-Yang zeros and large-deviation statistics of a molecular zipper

TL;DR

This paper uses Lee-Yang zeros derived from energy fluctuations in small molecular zippers to predict phase transitions and analyze large-deviation statistics, revealing a duality between small system fluctuations and thermodynamic phase behavior.

Contribution

It introduces a method to predict phase transitions in molecular zippers from finite-size energy fluctuations using Lee-Yang zeros, linking small system behavior to large-deviation statistics.

Findings

Energy fluctuations predict phase transition temperatures.

Lee-Yang zeros reveal large-deviation symmetry properties.

Small system fluctuations relate to thermodynamic phase behavior.

Abstract

The complex zeros of partition functions were originally investigated by Lee and Yang to explain the behavior of condensing gases. Since then, Lee-Yang zeros have become a powerful tool to describe phase transitions in interacting systems. Today, Lee-Yang zeros are no longer just a theoretical concept; they have been determined in recent experiments. In one approach, the Lee-Yang zeros are extracted from the high cumulants of thermodynamic observables at finite size. Here, we employ this method to investigate a phase transition in a molecular zipper. From the energy fluctuations in small zippers, we can predict the temperature at which a phase transition occurs in the thermodynamic limit. Even when the system does not undergo a sharp transition, the Lee-Yang zeros carry important information about the large-deviation statistics and its symmetry properties. Our work suggests an interesting duality between fluctuations in small systems and their phase behavior in the thermodynamic limit. These predictions may be tested in future experiments.