  Living systems are maintained out-of-equilibrium by external driving forces.
At stationarity, they exhibit emergent selection phenomena that break
equilibrium symmetries and originate from the expansion of the accessible
chemical space due to non-equilibrium conditions. Here, we use the matrix-tree
theorem to derive universal thermodynamic bounds on these symmetry-breaking
features in biochemical systems. Our bounds are independent of the kinetics and
hold for both closed and open reaction networks. We also extend our results to
master equations in the chemical space. Using our framework, we recover the
thermodynamic constraints in kinetic proofreading. Finally, we show that the
contrast of reaction-diffusion patterns can be bounded only by the
non-equilibrium driving force. Our results provide a general framework for
understanding the role of non-equilibrium conditions in shaping the
steady-state properties of biochemical systems.
