Living systems operate far from thermodynamic equilibrium, and understanding the fundamental constraints imposed by thermodynamic laws is crucial for unraveling the principles that govern life. This thesis investigates thermodynamic constraints on symmetry breaking in biochemical systems, elucidating how non-equilibrium conditions shape complex behaviors.

We introduce a novel concept called "thermodynamic space," which bounds the thermodynamically accessible phase space for biochemical systems operating at non-equilibrium stationary states. This concept allows us to quantify the degree of symmetry breaking in biochemical systems. We first prove the bound for linear and catalytic biochemical networks and then extend these results to generic chemical reaction networks. These bounds are applied to biological mechanisms such as kinetic proofreading, reaction-diffusion patterns, and self-assembly, providing insights into the thermodynamic costs of achieving specific biological functions. Our work also explores temporal asymmetries in non-equilibrium systems, establishing bounds on time-reversal asymmetry and investigating the thermodynamics of first passage times. These findings offer new tools for inferring non-equilibrium properties from partially observable quantities. Additionally, we present a minimal heat engine model that challenges conventional wisdom by achieving Carnot efficiency at maximum power output. This model provides insights into the remarkable efficiency of biological molecular machines and demonstrates the potential for harnessing collective advantage in energy transduction.

Our findings contribute to a deeper understanding of how non-equilibrium conditions enable and constrain life-like behaviors in biological and chemical systems. This work provides new tools for analyzing and predicting complex phenomena, with implications for understanding the fundamental principles governing life. The results may also inspire novel approaches in synthetic biology and nanotechnology, guiding the design of artificial systems with life-like properties.