Mechanical explanation of irreversible processes

Determine whether macroscopic irreversibility can be explained purely within classical mechanics by constructing a rigorous mechanical explanation of irreversible processes starting from microscopic dynamics of conservative systems. Clarify if and how the laws of mechanics account for the observed arrow of time without invoking non-mechanical assumptions.

Background

In the discussion of entropy and the second law, the paper raises the challenge of reconciling irreversible macroscopic behavior with the fundamentally reversible dynamics of classical mechanical systems. The author highlights the historical debate (e.g., Zermelo vs. Boltzmann) and the difficulty that ideal gases, obeying Newton’s laws, should exhibit reversible motion, which clashes with ubiquitous empirical irreversibility such as friction and diffusion.

This open problem situates the core question at the interface of thermodynamics and mechanics: can irreversibility be derived from microscopic mechanical laws without resorting to phenomenological or probabilistic postulates? The rest of the paper develops a systems-theoretic perspective using coupling to infinite-dimensional heat baths and stochastic modeling, but the fundamental mechanical derivation remains identified as unresolved.