Map entropy and the structural origins of irreversibility.

Abstract

The apparent contradiction between time-reversible microscopic dynamics and irreversible macroscopic behavior remains a cornerstone challenge in statistical mechanics. Traditional probabilistic models attribute entropy growth to systems evolving toward macrostates with more accessible microstates, yet they often fail to explain the mechanistic origins of irreversibility. We introduce map entropy, which reframes entropy growth as a structural consequence of any irreversible process that disperses energy into translational degrees of freedom. Through state-space transitions, it alters the configuration manifold via changes in particle number or momentum, expanding or pruning accessible microstates, consistent with Boltzmann's relation (S=k_{B}lnΩ), and unifies insights from nonequilibrium thermodynamics, reaction kinetics, and information theory. By applying map entropy to mechanical processes, chemical reactions, computational erasure, entropy of mixing, thermodynamic equilibration, and paradoxes such as Maxwell's demon, we demonstrate its predictive power and experimental testability, reframing the second law as a structural law rather than a statistical tendency.