H-theorem do-conjecture

TL;DR

This paper introduces a new conjecture related to the H-theorem, using a probabilistic and causal inference perspective, supported by numerical simulations and a toy model to illustrate entropy increase in classical systems.

Contribution

It formulates the H-theorem do-conjecture from a causal inference viewpoint and demonstrates its implications through simulations and a toy entropy game.

Findings

Numerical simulations support the causal effect of interventions on entropy.

The Ising-Conway Entropy Game illustrates entropy increase over time.

A probabilistic, causal perspective offers new insights into classical thermodynamics.

Abstract

A pedagogical formulation of Loschmidt's paradox and H-theorem is presented with basic notation on occupancy on discrete states without invoking velocity collision operators. A conjecture, so called H-theorem do-conjecture, is formulated. Causal inference perspective on the dynamical evolution of classical many-particle system is invoked. This perspectice introduce a probabilistic view on the state of the system conditioning on the thermodyamic ensemble, i.e., function of state-variables representing the ensemble. A numerical simulation of random walkers for deterministic diffusion demonstrate the causal effect of interventional ensemble, showing a dynamical behaviour as a test of the proposed conjecture. Moreover, the chosen game like dynamics provides an accessible practical example, named Ising-Conway Entropy Game, in order to demonstrate increase in entropy over time, as a toy system of statistical physics.