# Mechanochemical fluctuation theorem and thermodynamics of self-phoretic motors

## TL;DR

This paper investigates the thermodynamics and microscopic reversibility of self-phoretic nanomotors, deriving coupled Langevin equations and a fluctuation theorem, revealing reciprocal effects that enable fuel synthesis through mechanochemical coupling.

## Contribution

It introduces a mechanochemical fluctuation theorem for self-phoretic motors and links propulsion mechanisms to thermodynamic consistency and reciprocal effects.

## Key findings

- Derived coupled Langevin equations for nanomotor fluctuations
- Established a fluctuation theorem for reactive events and position
- Identified reciprocal effect enabling fuel synthesis

## Abstract

Microscopic dynamical aspects of the propulsion of nanomotors by self-phoretic mechanisms are considered. Propulsion by self-diffusiophoresis relies on the mechanochemical coupling between the fluid velocity field and the concentration fields induced by asymmetric catalytic reactions on the motor surface. The consistency between the thermodynamics of this coupling and the microscopic reversibility of the underlying molecular dynamics is investigated. For this purpose coupled Langevin equations for the translational, rotational, and chemical fluctuations of self-phoretic motors are derived. A mechanochemical fluctuation theorem for the joint probability to find the motor at position r after n reactive events have occurred during the time interval t is also derived. An important result that follows from this analysis is the identification of an effect that is reciprocal to self-propulsion by diffusiophoresis, which leads to the possibility of fuel synthesis by mechanochemical coupling to external force and torque.