# Microscopic Reversibility and Macroscopic Irreversibility: From a viewpoint of Algorithmic Randomness

## TL;DR

This paper demonstrates that in the Kac infinite chain model, microstates that are algorithmically random lead to irreversible macroscopic behavior, highlighting the role of randomness in the emergence of irreversibility.

## Contribution

It introduces a proof based on algorithmic randomness showing that Martin-Löf random microstates obey macroscopic irreversibility, connecting microscopic randomness to macroscopic laws.

## Key findings

- Martin-Löf random states satisfy macroscopic irreversibility.
- Time-reversed states of random microstates are not random and violate macroscopic laws.
- The approach links algorithmic randomness to the emergence of irreversibility.

## Abstract

Emergence of deterministic and irreversible macroscopic behavior from deterministic and reversible microscopic dynamics is understood as a result of the law of large numbers. In this paper, we prove on the basis of the theory of algorithmic randomness that Martin-L\"of random initial microstates satisfy an irreversible macroscopic law in the Kac infinite chain model. We find that the time-reversed state of a random state is not random as well as violates the macroscopic law.