# Thermodynamics of Reduced State of the Field

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## Abstract

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**2019**, 21, 705, a formalism aiming at describing macroscopic quantum fields, dubbed Reduced State of the Field (RSF), was envisaged. While, in the original work, a proper notion of entropy for macroscopic fields, together with their dynamical equations, was derived, here, we expand thermodynamic analysis of the RSF, discussing the notion of heat, solving dynamical equations in various regimes of interest, and showing the thermodynamic implications of these solutions.

## 1. Introduction

## 2. The RSF Formalism

## 3. Thermodynamics of the RSF

## 4. Some Examples of RSF Thermodynamics

#### 4.1. Free Dynamics of the RSF

#### 4.2. RSF Dynamics in Presence of a Coherent Source

#### 4.3. Dynamics of the RSF in Presence of a Coherent Source and a Thermal Bath

## 5. Conclusions

## Author Contributions

## Funding

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

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**Figure 1.**In this plot, the entropy as a function of temperature $\beta $ is shown. The various lines are plotted using different frequency, so that one can see that the low frequency modes contribute more to the entropy, especially at low temperatures.

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**MDPI and ACS Style**

Cusumano, S.; Rudnicki, Ł. Thermodynamics of Reduced State of the Field. *Entropy* **2021**, *23*, 1198.
https://doi.org/10.3390/e23091198

**AMA Style**

Cusumano S, Rudnicki Ł. Thermodynamics of Reduced State of the Field. *Entropy*. 2021; 23(9):1198.
https://doi.org/10.3390/e23091198

**Chicago/Turabian Style**

Cusumano, Stefano, and Łukasz Rudnicki. 2021. "Thermodynamics of Reduced State of the Field" *Entropy* 23, no. 9: 1198.
https://doi.org/10.3390/e23091198