Second-law-like inequalities with information and their interpretations

TL;DR

This paper compares various second-law-like inequalities incorporating information in thermodynamic processes with measurement and feedback, revealing a hierarchy and interconnections among different information measures.

Contribution

It introduces a hierarchy of information measures in thermodynamics, clarifying their origins and relationships through an analytically tractable feedback cooling model.

Findings

Information measures form a hierarchy with interconnections

Each measure corresponds to the minimal thermodynamic cost of specific measurement protocols

The study provides a unified framework for understanding information in thermodynamics

Abstract

In a thermodynamic process with measurement and feedback, the second law of thermodynamics is no longer valid. In its place, various second-law-like inequalities have been advanced that each incorporate a distinct additional term accounting for the information gathered through measurement. We quantitatively compare a number of these information measures using an analytically tractable model for the feedback cooling of a Brownian particle. We find that the information measures form a hierarchy that reveals a web of interconnections. To untangle their relationships, we address the origins of the information, arguing that each information measure represents the minimum thermodynamic cost to acquire that information through a separate, distinct measurement protocol.