Abstract: Living systems are constantly breaking symmetries in both space and time which are essential for many important biological processes, such as pattern formation, circadian rhythms, and high-precision discrimination. However, symmetry breaking also comes at a thermodynamic cost. In this talk, I will present new results on the thermodynamic costs of spatiotemporal symmetry breaking in living systems. First, I will show that universal thermodynamic constraints limit the degree of spatial symmetry breaking that can be achieved in biochemical systems [1]. By utilizing this framework, we elucidate the thermodynamic constraints in kinetic proofreading. Additionally, we demonstrate that the contrast of reaction-diffusion patterns can be exclusively limited by the non-equilibrium driving force. In the second part, I will show the thermodynamic cost of breaking temporal symmetries [2]. We derive thermodynamic bounds on relative propagators and combine them with stationary distribution to quantify the thermodynamic cost for time-reversal symmetry breaking. We apply our results to derive further thermodynamic constraints on the asymmetry of flux; on the asymmetry of finite-time cross-correlation; and on the cycle affinity of temporal coarse-grained dynamics. Our results suggest the minimum thermodynamic costs to achieve a certain degree of symmetry breaking in either space or time and can serve as design principles for engineering biochemical systems.

[1] Shiling Liang, Paolo De Los Rios, and Daniel Maria Busiello. “Universal thermodynamic bounds on symmetry breaking in biochemical systems”, arXiv, 2212,12074 (2022) 

[2] Shiling Liang and Simone Pigolotti. “Thermodynamic bounds on relative propagators and time-reversal asymmetry ” (under preparation, will be on arXiv soon)