# Reflections on Friction in Quantum Mechanics

## Abstract

**:**

**PACS**03.65.-w,05.40.-a,05.70.Ln

- External friction amounts to the dissipation of kinetic energy from a small “open system” to its environment, creating entropy and heat. The relevance of kinetic energy is related to the isotropy of the environment, and the asymmetry of a particular direction of (non-zero) velocity. Irreversibility and the generation of heat and entropy are related to the disparity in the size and time scales of the systems, leading to effective irreversible memoryless dynamics and a large entropy generation. Heuristically, external friction is the attempt by the environment to lower the system to a “symmetric” velocity of zero.
- Internal friction, which is the generation of excitations (which are then typically dissipated by external friction) due to the disparity between the internal time-scales of the system and the external driving time scale. Heuristically, internal friction is the resistance of the system to rapid change.

## 1. Internal Friction

**Figure 1.**The Shannon energy entropy ${S}_{E}$ for a fixed frequency $\u0127\omega =1$, as a function of the energy E in units of $\u0127\omega $. In a quasistatic process from some initial thermal state we will reach some final energy and therefore entropy at the final frequency, represented by point A. A faster process reaching the same final frequency will generally result in higher energy, represented by point B. The slope $dS/dE$ at point B is lower than in point A, and therefore the inverse slope $dE/dS$ will be higher. Using the thermodynamic identification $T=dE/dS$, this figure shows that non-quasistatic dynamics will yield higher temperatures.

## 2. Dissipation to the Environment

## 3. Brownian Motion

## 4. Quantum Fluctuations

## 5. Discussion

## Acknowledgments

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Rezek, Y. Reflections on Friction in Quantum Mechanics. *Entropy* **2010**, *12*, 1885-1901.
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Rezek Y. Reflections on Friction in Quantum Mechanics. *Entropy*. 2010; 12(8):1885-1901.
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**Chicago/Turabian Style**

Rezek, Yair. 2010. "Reflections on Friction in Quantum Mechanics" *Entropy* 12, no. 8: 1885-1901.
https://doi.org/10.3390/e12081885