# Thermodynamic entropy of a many body energy eigenstate

## TL;DR

This paper argues that individual many-body energy eigenstates have well-defined thermodynamic entropy, which can be derived from entanglement entropy between subsystems, linking quantum states to thermodynamic behavior.

## Contribution

It introduces a method to explicitly construct thermodynamic entropy from wave functions by analyzing entanglement entropy between subsystems.

## Key findings

- Eigenstates exhibit thermodynamic characteristics similar to isolated systems.
- Entanglement entropy between subsystems corresponds to thermodynamic entropy per degree of freedom.
- Subsystems can exchange heat while remaining in an energy eigenstate during adiabatic evolution.

## Abstract

It is argued that a typical many body energy eigenstate has a well defined thermodynamic entropy and that individual eigenstates possess thermodynamic characteristics analogous to those of generic isolated systems. We examine large systems with eigenstate energies equivalent to finite temperatures. When quasi-static evolution of a system is adiabatic (in the quantum mechanical sense), two coupled subsystems can transfer heat from one subsystem to another yet remain in an energy eigenstate. To explicitly construct the entropy from the wave function, degrees of freedom are divided into two unequal parts. It is argued that the entanglement entropy between these two subsystems is the thermodynamic entropy per degree of freedom for the smaller subsystem. This is done by tracing over the larger subsystem to obtain a density matrix, and calculating the diagonal and off-diagonal contributions to the entanglement entropy.