Thermodynamics of large-scale chemical reaction networks

TL;DR

This paper introduces tensor network methods to efficiently analyze the thermodynamics of large-scale, stochastic chemical reaction networks, enabling accurate computation of thermodynamic quantities without high-dimensional sampling.

Contribution

It demonstrates the use of tensor networks to directly solve the chemical master equation, overcoming computational challenges and providing precise thermodynamic insights.

Findings

Accurate estimates of entropy production, heat flux, and chemical work.

Tensor networks enable sub-exponential computational cost for large systems.

Application to a dissipative self-assembly model illustrates practical utility.

Abstract

Chemical and biological networks can describe a wide variety of processes, from gene regulatory networks to biochemical oscillations. Modeled by chemical master equations, these processes are inherently stochastic, as fluctuations dominate deterministic order at mesoscopic scales. These classic many-body processes suffer from the so-called curse of high dimensionality, which makes exact mathematical descriptions exponentially expensive to compute. The exponential cost renders the study of the thermodynamic properties of such systems out of equilibrium intractable and forces approximations of system noise or assumptions of continuous particle numbers. Here, we use tensor networks to numerically explore the thermodynamics of chemical processes by directly solving the ensemble solution of the chemical master equation with efficient (sub-exponential) computational cost. We provide accurate estimates of the entropy production rate, heat flux, chemical work, and nonequilibrium thermodynamic potentials, free from sampling errors or mean-field approximations. We illustrate our results through a dissipative self-assembly model. In this way, we show how tensor networks can inform the design of efficient chemical processes in previously unattainable regimes.