Necessary and sufficient condition for stability of generalized expectation value

TL;DR

This paper establishes the necessary and sufficient condition for the stability of a broad class of generalized expectation values used in nonequilibrium statistical mechanics when the underlying probability distribution is slightly altered.

Contribution

It provides a precise criterion for stability of generalized expectation values, enhancing understanding of their robustness in complex systems.

Findings

Derived a necessary and sufficient condition for stability

Applicable to a wide class of generalized expectation definitions

Improves theoretical foundation for nonequilibrium statistical mechanics

Abstract

A class of generalized definitions of expectation value is often employed in nonequilibrium statistical mechanics for complex systems. Here, the necessary and sufficient condition is presented for such a class to be stable under small deformations of a given arbitrary probability distribution.