# Heating without heat: thermodynamics of passive energy filters between finite systems

## TL;DR

This paper explores how passive energy filters can transfer particles between finite systems to alter their temperatures without external energy input, challenging traditional thermodynamic expectations.

## Contribution

It demonstrates that passive filters can induce temperature changes in systems without violating the second law, revealing novel thermodynamic behaviors.

## Key findings

- Passive filters can increase or decrease system temperatures without energy input.
- Selective particle transfer can occur between systems with different average energies.
- Thermodynamic cycles can achieve temperatures below or above initial reservoir temperatures.

## Abstract

Passive filters allowing the exchange of particles in a narrow band of energy are currently used in micro-refrigerators and energy transducers. In this letter, we analyze their thermal properties using linear irreversible thermodynamics and kinetic theory, and discuss a striking phenomenon: the possibility of increasing or decreasing simultaneously the temperatures of two systems without any supply of energy. This occurs when the filter induces a flow of particles whose energy is between the average energies of the two systems. Here we show that this selective transfer of particles does not need the action of any sort of Maxwell demon and can be carried out by passive filters without compromising the second law of thermodynamics. The phenomenon allows us to design cycles between two reservoirs at temperatures $T_1<T_2$ that are able to reach temperatures below $T_1$ or above $T_2$.