**Preamble**

Probably, one of the most fundamental issue in classical statistical mechanics is extending reversible dynamics to many-particle systems that behaves irreversibly. In other words, how time's arrow appears even though constituted systems evolves in reversible dynamics. This is the main idea of Loschmidt's paradox. The resolution to this paradox lies into something called *interventional thermodynamic ensembles (ITEs). *

Leaning Tower of Pisa:Recall Galileo's Experiments (Wikipedia) |

Time-asymmetry is about different histories : Counterfactual dynamics

Time-asymmetry is about different histories : Counterfactual dynamics

Before trying to understand how ITEs are used in resolving Loschmidt's paradox, we understand that inducing different trajectories on an identical dynamical system in "a parallel universe" implies time-asymmetry. A trajectory provides here a reversibility. So called "a parallel universe" is about imagining a different dynamics via a sampling, this corresponds to *counterfactuals* within Causal inference frameworks.

**Interventional Thermodynamic Ensembles (ITEs)**

Interventional ensemble build upon an other ensemble, for the sake of simplicity, we can think of an ensemble as an associated chosen sampling scheme. From this perspective, sampling scheme $\mathscr{E}$ would have an interventional sampling $do(\mathscr{E})$ if the adjusted scheme only introduces a change in the scheme that doesn't change the inherent dynamics but effects the dynamical history. One of the first examples of this is appeared recently: *single-spin-flip *vs. *dual-spin-flip *dynamics [suezen23]. This is shown with simulations.

**Outlook**

Reversibility and time-asymmetry in classical dynamics are a long standing issues in physics. By inducing causal inference perspective in computing dynamical evolution of many body systems leads to reconciliation of reversibility and time-asymmetry i.e., $do-$operator's interpretation.

**References**

[suezen23] H-theorem do-conjecture (2023) arXiv:2310.01458 (simulation code GitHub).