# Backward non-unitary quantum evolution

## TL;DR

This paper introduces a nonlinear backward equation linked to Bohmian quantum potential, exploring its implications for probability non-conservation, Onsager's relations, and the optical theorem in non-equilibrium quantum systems.

## Contribution

It proposes a novel nonlinear backward equation and Schrödinger equation framework for analyzing non-unitary quantum evolution and extends the analysis to multi-particle systems.

## Key findings

- Probability is not conserved in non-equilibrium regimes.
- The formalism impacts Onsager's relations and the optical theorem.
- Extension to multi-particle systems is outlined.

## Abstract

A non-linear backward equation with diffusive terms is postulated for the probability density that depends on the Bohmian quantum potential. An associated nonlinear Schr\"{o}dinger equation is also introduced and extension of the analysis to several particle compounds is sketched along with the implications following from this formalism regarding the non-conservation of probability in the non-equilibrium regime. Some further conclusions are educed with respect to the Onsager's relations and the generalized optical theorem.