# The Free Energy of a General Computation

## TL;DR

This paper explores the thermodynamic costs of computation, linking information erasure to free energy, and generalizes Landauer's principle to broader computational processes, while reinterpreting the second law of thermodynamics through a computational lens.

## Contribution

It introduces a generalized bound on free energy for any computation and connects thermodynamic principles with the logical reversibility of time evolution.

## Key findings

- Erasure cost equals the length of optimal reversible compression.
- Bounds on free energy investment for general computations are established.
- Revisiting the second law reveals a logico-informational perspective with simulation resilience.

## Abstract

Starting from Landauer's slogan "information is physical," we revise and modify Landauer's principle stating that the erasure of information has a minimal price in the form of a certain quantity of free energy. We establish a direct link between the erasure cost and the work value of a piece of information, and show that the former is essentially the length of the string's best compression by a reversible computation. We generalize the principle by deriving bounds on the free energy to be invested for --- or gained from, for that matter --- a general computation. We then revisit the second law of thermodynamics and compactly rephrase it (assuming the Church/Turing/Deutsch hypothesis that physical reality can be simulated by a universal Turing machine): Time evolutions are logically reversible --- "the future fully remembers the past (but not necessarily vice versa)." We link this view to previous formulations of the second law, and we argue that it has a particular feature that suggests its "logico-informational" nature, namely simulation resilience: If a computation faithfully simulates a physical process violating the law --- then that very computation procedure violates it as well.