# Quantum thermodynamics from the nonequilibrium dynamics of open systems: energy, heat capacity and the third law

## TL;DR

This paper investigates the conditions under which quantum thermodynamics is well-defined for open quantum systems, using exact solutions of quantum Brownian motion to analyze energy, heat capacity, and the Third Law, challenging previous claims about negative specific heat and entanglement.

## Contribution

It provides a systematic open system approach to quantum thermodynamics, deriving conditions for thermodynamic laws and analyzing a solvable model to clarify misconceptions about heat capacity and the Third Law.

## Key findings

- Internal energy is extensive in the studied models.
- Heat capacity remains positive down to zero temperature.
- The Third Law holds in the examined quantum systems.

## Abstract

We take the perspective of open quantum systems and examine from their nonequilibrium dynamics the conditions when the physical quantities, their relations and the laws of thermodynamics become well defined and viable for quantum many body systems. We first describe how an open system nonequilibrium dynamics (ONEq) approach is different from the closed combined system + environment in a global thermal state (CGTs) setup. Only after the open system equilibrates will it be amenable to conventional thermodynamics descriptions, thus quantum thermodynamics (QTD) comes at the end rather than assumed in the beginning. We see the open system approach having the advantage of dealing with nonequilibrium processes as many experiments in the near future will call for. Because it spells out the conditions of QTD's existence it can also aid us in addressing the basic issues in quantum thermodynamics from first principles in a systematic way. We then study one broad class of open quantum systems where the full nonequilibrium dynamics can be solved exactly, that of the quantum Brownian motion of $N$ strongly coupled harmonic oscillators, interacting strongly with a scalar field environment. Here we focus on the internal energy, heat capacity and the Third Law. We show for this class of physical models, amongst other findings, the extensive property of the internal energy, the positivity of the heat capacity and the validity of the Third Law from the perspective of the behavior of the heat capacity toward zero temperature. These conclusions obtained from exact solutions and quantitative analysis clearly disprove claims of negative specific heat in such systems and dispel allegations that in such systems the validity of the Third Law of thermodynamics relies on quantum entanglement.