Statistical ensembles without typicality

TL;DR

This paper offers a new operational derivation of maximum-entropy ensembles in statistical mechanics, showing they naturally arise from the set of possible system-environment transitions under partial information, without relying on typicality.

Contribution

It introduces an operational framework that justifies maximum-entropy ensembles based on allowed transitions, avoiding typicality or information-theoretic assumptions.

Findings

Allowed transitions match those with maximum entropy states

Provides a derivation of ensembles from operational principles

Justifies the use of maximum-entropy ensembles without typicality

Abstract

Maximum-entropy ensembles are key primitives in statistical mechanics from which thermodynamic properties can be derived. Over the decades, several approaches have been put forward in order to justify from minimal assumptions the use of these ensembles in statistical descriptions. However, there is still no full consensus on the precise reasoning justifying the use of such ensembles. In this work, we provide a new approach to derive maximum-entropy ensembles taking a strictly operational perspective. We investigate the set of possible transitions that a system can undergo together with an environment, when one only has partial information about both the system and its environment. The set of all these allowed transitions encodes thermodynamic laws and limitations on thermodynamic tasks as particular cases. Our main result is that the set of allowed transitions coincides with the one possible if both system and environment were assigned the maximum entropy state compatible with the partial information. This justifies the overwhelming success of such ensembles and provides a derivation without relying on considerations of typicality or information-theoretic measures.