# Osmotic pressure of matter and vacuum energy

## TL;DR

This paper explores how matter-vacuum interactions modify osmotic pressure in a confined system, revealing a vacuum-induced negative pressure that reduces the effective osmotic pressure, with parallels in superfluid helium experiments.

## Contribution

It introduces a novel effect where vacuum interactions alter osmotic pressure, distinct from Casimir effects, applicable in thermodynamic limits and analogous to superfluid helium phenomena.

## Key findings

- Vacuum interaction induces a negative pressure inside the box.
- Measured osmotic pressure is reduced due to vacuum effects.
- The effect is independent of the box size in the thermodynamic limit.

## Abstract

The walls of the box which contains matter represent a membrane that allows the relativistic quantum vacuum to pass but not matter. That is why the pressure of matter in the box may be considered as the analog of the osmotic pressure. However, we demonstrate that the osmotic pressure of matter is modified due to interaction of matter with vacuum. This interaction induces the nonzero negative vacuum pressure inside the box, as a result the measured osmotic pressure becomes smaller than the matter pressure. As distinct from the Casimir effect, this induced vacuum pressure is the bulk effect and does not depend on the size of the box. This effect dominates in the thermodynamic limit of the infinite volume of the box. Analog of this effect has been observed in the dilute solution of 3He in liquid 4He, where the superfluid 4He plays the role of the non-relativistic quantum vacuum, and 3He atoms play the role of matter.