# Finite-time adiabatic processes: derivation and speed limit

## TL;DR

This paper develops a method to construct finite-time adiabatic processes for Brownian particles by controlling potential and temperature, and establishes a fundamental speed limit dictated by the second law of thermodynamics.

## Contribution

It provides a systematic way to engineer finite-time adiabatic processes and derives an explicit speed limit for such transformations.

## Key findings

- Finite-time adiabatic processes can be explicitly constructed for Brownian particles.
- A minimum time for adiabatic transformations is derived from the second law.
- The speed limit depends on the system's initial and final states.

## Abstract

Obtaining adiabatic processes that connect equilibrium states in a given time represents a challenge for mesoscopic systems. In this paper, we explicitly show how to build these finite-time adiabatic processes for an overdamped Brownian particle in an arbitrary potential, a system that is relevant both at the conceptual and the practical level. This is achieved by jointly engineering the time evolutions of the binding potential and the fluid temperature. Moreover, we prove that the second principle imposes a speed limit for such adiabatic transformations: there appears a minimum time to connect the initial and final states. This minimum time can be explicitly calculated for a general compression/decompression situation.