Scaling in Biological Systems: A Molecular-Ensemble Duality.

We have observed in muscle the statistical mechanics of irreversible chemical thermodynamics, revealing the solution to multiple seemingly unrelated paradoxes in science. Analogous to Boltzmann's H theorem, we observe that chemical reaction energy landscapes (ensemble entropic wells) irreversibly evolve over time, pulling reversible chemical reactions forward in time. Loschmidt's paradox assumes that reversible molecular reactions scale up to irreversible changes in an ensemble, and many mathematical constructs have been created to satisfy this assumption (Boltzmann's H-function, chemical activities, the kinetics theory of gases, molecular mechanisms of biological function, etc.). However, using a simple statistical argument, here we show that the irreversible time evolutions of molecular and ensemble states are described by two different non-scalable entropies, creating a molecular-ensemble duality in any system on any scale. This inverts common understandings of mechanistic agency and the arrow of time and disproves all molecular mechanisms of irreversible ensemble processes.