# Energy Dissipation Bounds for Autonomous Thermodynamic Cycles

## TL;DR

This paper derives bounds on energy dissipation in autonomous thermodynamic cycles, revealing that even infinitely slow processes can be energetically irreversible due to combined effects of thermodynamic friction and control precision costs.

## Contribution

It introduces a stochastic thermodynamics framework to quantify energy costs considering both thermodynamic friction and control precision, challenging traditional adiabatic assumptions.

## Key findings

- Energy dissipation bounds depend on both friction and control precision.
- Infinitely slow protocols are not necessarily reversible energetically.
- Autonomous control introduces fundamental irreversibility in thermodynamic cycles.

## Abstract

How much free energy is irreversibly lost during a thermodynamic process? For deterministic protocols, lower bounds on energy dissipation arise from the thermodynamic friction associated with pushing a system out of equilibrium in finite time. Recent work has also bounded the cost of precisely moving a single degree of freedom. Using stochastic thermodynamics, we compute the total energy cost of an autonomously controlled system by considering both thermodynamic friction and the entropic cost of precisely directing a single control parameter. Our result suggests a challenge to the usual understanding of the adiabatic limit: here, even infinitely slow protocols are energetically irreversible.