# Overview of Information Theory, Computer Science Theory, and Stochastic Thermodynamics for Thermodynamics of Computation

## TL;DR

This paper reviews the theoretical foundations linking information theory, computational models, and non-equilibrium thermodynamics to analyze the entropy flow in computational systems, emphasizing the impact of global structure on thermodynamic costs.

## Contribution

It introduces an exact expression for entropy flow in non-equilibrium systems and applies it to analyze thermodynamic aspects of reversible and irreversible computation.

## Key findings

- Exact entropy flow expression derived from non-equilibrium statistical physics
- Analysis of entropy costs in reversible vs irreversible computation
- Insights into how system structure influences thermodynamic efficiency

## Abstract

I give a quick overview of some of the theoretical background necessary for using modern non-equilibrium statistical physics to investigate the thermodynamics of computation. I first present some of the necessary concepts from information theory, and then introduce some of the most important types of computational machine considered in computer science theory. After this I present a central result from modern non-equilibrium statistical physics: an exact expression for the entropy flow out of a system undergoing a given dynamics with a given initial distribution over states. This central expression is crucial for analyzing how the total entropy flow out of a computer depends on its global structure, since that global structure determines the initial distributions into all of the computer's subsystems, and therefore (via the central expression) the entropy flows generated by all of those subsystems. I illustrate these results by analyzing some of the subtleties concerning the benefits that are sometimes claimed for implementing an irreversible computation with a reversible circuit constructed out of Fredkin gates.