A holographic map of action onto entropy

TL;DR

This paper proposes a holographic relationship linking the action in a bulk system to the entropy of its boundary, suggesting a deep connection between thermodynamics and quantum mechanics.

Contribution

It introduces a novel holographic correspondence between action and entropy, connecting thermodynamics, quantum uncertainty, and holography in a unified framework.

Findings

Establishes a relation between action and entropy in holographic systems

Links the second law of thermodynamics with the quantum uncertainty principle

Proposes units of measurement for action and entropy in this context

Abstract

We propose a holographic correspondence between the action integral I describing the mechanics of a finite number of degrees of freedom in the bulk, and the entropy S of the boundary (a holographic screen) enclosing that same volume. The action integral must be measured in units of (i times) Planck's constant, while the entropy must be measured in units of Boltzmann's constant. In this way we are led to an intriguing relation between the second law of thermodynamics and the uncertainty principle of quantum mechanics.