The mechanics of cells and tissues are largely governed by scaffolds of
filamentous proteins that make up the cytoskeleton, as well as
extracellular matrices. Evidence is emerging that such networks can
exhibit rich mechanical phase behavior. A classic example of a
mechanical phase transition was identified by Maxwell for macroscopic
engineering structures: networks of struts or springs exhibit a
continuous, second-order phase transition at the isostatic point, where
the number of constraints imposed by connectivity just equals the number
of mechanical degrees of freedom. We will present recent theoretical
predictions and experimental evidence for mechanical phase transitions
in both synthetic and biopolymer networks. Living systems typically
operate far from thermodynamic equilibrium, which affects both their
dynamics and mechanical response. As a result of enzymatic activity at
the molecular scale, living systems characteristically violate detailed
balance, a fundamental principle of equilibrium statistical mechanics.
We discuss fundamental non-equilibrium signatures of living systems,
including violations of detailed balance at the meso-scale of whole cells