# Energetic instability of passive states in thermodynamics

## TL;DR

This paper demonstrates that, unlike thermal states, all other passive states are energetically unstable under reversible processes, highlighting the unique stability of thermal states and their connection to temperature in quantum thermodynamics.

## Contribution

It shows that only thermal states are stable passive states under reversible processes in single systems, providing a new single-shot perspective on thermodynamic temperature.

## Key findings

- All passive states except thermal states are energetically unstable.
- Optimal work extraction from passive states operates at Carnot efficiency.
- A virtual reservoir model explains work extraction from passive states.

## Abstract

Passivity is a fundamental concept in thermodynamics that demands a quantum system's energy cannot be lowered by any reversible, unitary process acting on the system. In the limit of many such systems, passivity leads in turn to the concept of complete passivity, thermal states, and the emergence of a thermodynamic temperature. In contrast, here we need only consider a single system and show that every passive state except the thermal state is unstable under a weaker form of reversibility. More precisely, we show that given a single copy of any athermal quantum state we may extract a maximal amount of energy from the state when we can use a machine that operates in a reversible cycle and whose state is left unchanged. This means that for individual systems the only form of passivity that is stable under general reversible processes is complete passivity, and thus provides a single-shot and more physically motivated identification of thermal states and the emergence of temperature. The machine which extracts work from passive states exploits the fact that one can find a subspace which acts as a virtual hot reservoir, and a subspace which acts as a virtual cold reservoir. We show that an optimal amount of work can be extracted, and that the machine operates at the Carnot efficiency between pairs of virtual reservoirs.