Universal thermodynamic bounds on spontaneous chiral symmetry breaking

Living systems are constituted by biomolecules of one single-handedness. However, due to mirror symmetry, the mirror copy of current living systems should have the same physical and chemical properties. The spontaneous origin of this observed chirality in living systems remains a fundamental mystery in the origin of life. In the past years, many non-linear chemical reaction schemes have been proposed to show the emergence of spontaneous chiral symmetry breaking (SCSB). Nevertheless, most of these models lack thermodynamic consistency due to the presence of unidirectional reaction paths, while the remaining ones have not been investigated in terms of universal thermodynamic properties but mainly focus on model-specific properties. Here, we build several thermodynamically consistent nonequilibrium reaction networks and investigate their thermodynamic properties and bounds under SCSB. Apart from the common setup in which a chemical force drives the system away from equilibrium, we show that a temperature gradient can also act as a non-equilibrium driving force to trigger SCSB in a fully closed reaction system. Such a non-isothermal driving force may be a more plausible scenario in the early stages of chemical evolution. In our framework, the SCSB is explained as a selection of reaction pathways due to catalytic reactions: chiral species modulate the dynamics of the reaction network via catalysis and select the driving reaction path that maximizes the chiral asymmetry. We also find that the degree of chiral asymmetry is bounded by the maximal thermodynamic force applied to the system. This bound is universal for catalytic reaction networks and it relies only on equilibrium quantities evaluated on one single spanning tree.