# Entropy, Carnot Cycle and Information Theory, Part 2

## TL;DR

This paper explores the Carnot cycle through thermodynamics and information theory, highlighting how entropy and energy concepts relate to information processes.

## Contribution

The paper introduces new interpretations of free energy and entropy in thermodynamics and applies them to information theory.

## Key findings

- A new interpretation of free energy in isothermal expansion is presented.
- Entropy in the adiabatic phase is reinterpreted in thermodynamics.
- An information theory cycle is constructed using Lagrange parameters and codeword length.

## Abstract

This second part of this companion paper the Carnot cycle is analyzed trying to investigate the similarities and differences between a framework related to thermodynamics and one related to information theory. The parametric Schrodinger equations are the starting point for the framing. In the thermodynamics frame, a new interpretation of the free energy in the isothermal expansion and a new interpretation of the entropy in the adiabatic phase are highlighted. The same Schrodinger equations are then applied in an information theory framework. Again, it is shown that a cycle can be constructed with a diagram that presents the Lagrange parameter and the average codeword length as coordinates. In this case the adiabatic phase consists of a transcoding operation and the cycle as a whole shows a positive or negative balance of information. In conclusion, the Carnot cycle continues to be a source of knowledge of complex systems in which entropy plays a central role.