# Hybrid Einstein-Langevin Approach for Microscopic formulation of Viscous Drag: An Alternative to the Langevin Equation

## TL;DR

This paper introduces a thermodynamic hybrid approach that models Brownian motion without stochastic forces, using system-intrinsic microwork and microforces to unify microscopic and macroscopic descriptions.

## Contribution

It proposes a novel thermodynamic framework replacing the Langevin equation with system-intrinsic microwork and microforces for microscopic motion analysis.

## Key findings

- Provides a microstate-specific equation of motion.
- Ensures the equipartition theorem is always satisfied.
- Offers a unified approach to fluctuations across scales.

## Abstract

We present a novel hybrid but thermodynamic approach to provide an alternative to the Langevin equation by using system-intrinsic (SI) microwork done by the Brownian particle in the kth microstate (realization). The corresponding SI-microforce is unique to the microstate and determines the microscopic equation of motion for it. Being a thermodynamic approach, the equipartition theorem is always satisfied and no additional stochastic Langevin force is needed. We determine instantaneous and long-time averages of useful quantities and thus provide a new unified approach to the fluctuating motion from mesoscopic to macroscopic scales.