Stochastic thermodynamics: From principles to the cost of precision

TL;DR

This paper develops the principles of stochastic thermodynamics, focusing on entropy production, fluctuation theorems, and bounds on the cost-precision trade-off in biomolecular systems, with applications to molecular motors and enzymatic networks.

Contribution

It introduces a comprehensive framework connecting stochastic thermodynamics principles to the thermodynamic uncertainty relation and its applications to biological systems.

Findings

Universal bounds on large deviation rate functions derived.

Thermodynamic uncertainty relation generalized for biomolecular processes.

Tools for thermodynamic inference of hidden system properties provided.

Abstract

In these lecture notes, the basic principles of stochastic thermodynamics are developed starting with a closed system in contact with a heat bath. A trajectory undergoes Markovian transitions between observable meso-states that correspond to a coarse-grained description of, e.g., a biomolecule or a biochemical network. By separating the closed system into a core system and into reservoirs for ligands and reactants that bind to, and react with the core system, a description as an open system controlled by chemical potentials and possibly an external force is achieved. Entropy production and further thermodynamic quantities defined along a trajectory obey various fluctuation theorems. For describing fluctuations in a non-equilibrium steady state in the long-time limit, the concept of a rate function for large deviations from the mean behaviour is derived from the weight of a trajectory. Universal bounds on this rate function follow which prove and generalize the thermodynamic uncertainty relation that quantifies the inevitable trade-off between cost and precision of any biomolecular process. Specific illustrations are given for molecular motors, Brownian clocks and enzymatic networks that show how these tools can be used for thermodynamic inference of hidden properties of a system.