# Work drives time evolution

## TL;DR

This paper proposes that the time evolution of quantum systems is driven by extractible work rather than energy, challenging traditional quantum mechanics and linking to a gravity theory based on work.

## Contribution

It introduces a novel formalism where extractible work, not the Hamiltonian, governs quantum dynamics, with implications for quantum mechanics and gravitation theories.

## Key findings

- Expectations of occupation numbers deviate from standard quantum mechanics.
- The formalism connects quantum dynamics with a gravity theory based on work.
- Discussion on scope, applications, and validity of the proposal.

## Abstract

We propose the idea that time evolution of quantum systems is driven by work. The formalism presented here falls within the scope of a recently proposed theory of gravitating quantum matter where extractible work, and not energy, is responsible for gravitation. Our main assumption is that extractible work, and not the Hamiltonian, dictates dynamics. We find that expectation values of meaningful quantities, such as the occupation number, deviate from those predicted by standard quantum mechanics. The scope, applications and validity of this proposal are also discussed.