Thermodynamic characterization of message-passing: Framework and initial study

Abstract

We study the thermodynamic efficiency of message-passing decoders using the mismatch cost framework. This framework quantifies the excess entropy generated when a system operates away from the thermodynamically optimal initial distribution. It provides a computable lower bound on irrecoverable energy loss. The decoder is modeled as a main decoding program with local message updates implemented as subroutines. Memory is treated as an external copying subsystem whose thermodynamic cost is excluded. Studying the $[7,4]$ Hamming code transmitted over a binary erasure channel, we show how the channel-induced initialization statistics and the step-wise evolution of the algorithmic state distribution during decoding determine the total mismatch cost. We further show that different thermodynamically optimal state distributions, representing different underlying physical implementations of the decoder, can produce different thermodynamic costs for identical decoding dynamics. Conditioning the input distribution on correctable and non-correctable erasure patterns further reveals distinct thermodynamic signatures. These results demonstrate that thermodynamic cost is jointly governed by decoding dynamics, input statistics, and hardware characteristics. This points to opportunities for thermodynamically-informed decoder design to realize energy-efficient physical implementations.

arXiv commentPublished in IEEE Journal on Selected Areas in Information Theory (JSAIT), August 2026. 36 pages, 10 figures

References in corpus (10)

• Stochastic thermodynamics, fluctuation theorems, and molecular machines
• Ensemble and Trajectory Thermodynamics: A Brief Introduction
• Thermodynamic Unification of Optimal Transport: Thermodynamic Uncertainty Relation, Minimum Dissipation, and Thermodynamic Speed Limits
• Stochastic thermodynamics of computation
• The thermodynamic efficiency of computations made in cells across the range of life
• Thermodynamics of computing with circuits
• Is stochastic thermodynamics the key to understanding the energy costs of computation?
• Dependence of dissipation on the initial distribution over states
• Principles of Low Dissipation Computing from a Stochastic Circuit Model
• Thermodynamics of computations with absolute irreversibility, unidirectional transitions, and stochastic computation times