Effective Affinity for Generic Currents in Markov Processes

TL;DR

This paper introduces the concept of effective affinity for generic currents in Markov processes, capturing dissipative and fluctuation properties, and relates it to stalling forces in biological motor models.

Contribution

It defines an effective affinity applicable to multiple coupled currents, extending thermodynamic concepts beyond uncoupled systems, with theoretical and biological implications.

Findings

Effective affinity determines current direction.

It bounds dissipation rates and constrains fluctuations.

In certain models, effective affinity equals stalling force.

Abstract

In nonequilibrium systems with uncoupled currents, the thermodynamic affinity determines the direction of currents, quantifies dissipation, and constrains current fluctuations. However, these properties of the thermodynamic affinity do not hold in complex systems with multiple coupled currents. For this reason, there has been an ongoing search in nonequilibrium thermodynamics for an affinity-like quantity, known as the effective affinity, which applies to a single current in a system with multiple coupled currents. Here, we introduce an effective affinity that applies to generic currents in time-homogeneous Markov processes. We show that the effective affinity is a single number encapsulating several dissipative and fluctuation properties of fluctuating currents: the effective affinity determines the direction of flow of the current; the effective affinity multiplied by the current is a lower bound for the rate of dissipation; for systems with uncoupled currents the effective affinity equals the standard thermodynamic affinity; and the effective affinity constrains negative fluctuations of currents, namely, it is the exponential decay constant of the distribution of current infima. We derive the above properties with large deviation theory and martingale theory, and one particular interesting finding is a class of martingales associated with generic currents. Furthermore, we make a study of the relation between effective affinities and stalling forces in a biomechanical model of motor proteins, and we find that both quantities are approximately equal when this particular model is thermodynamically consistent. This brings interesting perspectives on the use of stalling forces for the estimation of dissipation.