Next Article in Journal
Application of the Generalized Work Relation for an N-level Quantum System
Next Article in Special Issue
Panel I: Connecting 2nd Law Analysis with Economics, Ecology and Energy Policy
Previous Article in Journal
Identifying the Coupling Structure in Complex Systems through the Optimal Causation Entropy Principle
Previous Article in Special Issue
Gyarmati’s Variational Principle of Dissipative Processes
Entropy 2014, 16(6), 3434-3470; doi:10.3390/e16063434

Some Trends in Quantum Thermodynamics

1,*  and 2
1 Mechanical Engineering Department, Virginia Tech, Blacksburg, VA 24061, USA 2 Physics Department, University of Osnabrueck, Barbarastrasse 7, 49069 Osnabrueck, Germany
* Author to whom correspondence should be addressed.
Received: 28 February 2014 / Revised: 23 April 2014 / Accepted: 10 June 2014 / Published: 23 June 2014
View Full-Text   |   Download PDF [789 KB, uploaded 24 February 2015]   |   Browse Figures


Traditional answers to what the 2nd Law is are well known. Some are based on the microstate of a system wandering rapidly through all accessible phase space, while others are based on the idea of a system occupying an initial multitude of states due to the inevitable imperfections of measurements that then effectively, in a coarse grained manner, grow in time (mixing). What has emerged are two somewhat less traditional approaches from which it is said that the 2nd Law emerges, namely, that of the theory of quantum open systems and that of the theory of typicality. These are the two principal approaches, which form the basis of what today has come to be called quantum thermodynamics. However, their dynamics remains strictly linear and unitary, and, as a number of recent publications have emphasized, “testing the unitary propagation of pure states alone cannot rule out a nonlinear propagation of mixtures”. Thus, a non-traditional approach to capturing such a propagation would be one which complements the postulates of QM by the 2nd Law of thermodynamics, resulting in a possibly meaningful, nonlinear dynamics. An unorthodox approach, which does just that, is intrinsic quantum thermodynamics and its mathematical framework, steepest-entropy-ascent quantum thermodynamics. The latter has evolved into an effective tool for modeling the dynamics of reactive and non-reactive systems at atomistic scales. It is the usefulness of this framework in the context of quantum thermodynamics as well as the theory of typicality which are discussed here in some detail. A brief discussion of some other trends such as those related to work, work extraction, and fluctuation theorems is also presented.
Keywords: quantum thermodynamics; non-equilibrium; 2nd Law of thermodynamics quantum thermodynamics; non-equilibrium; 2nd Law of thermodynamics
This is an open access article distributed under the Creative Commons Attribution License (CC BY) which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Share & Cite This Article

Further Mendeley | CiteULike
Export to BibTeX |
EndNote |
MDPI and ACS Style

von Spakovsky, M.R.; Gemmer, J. Some Trends in Quantum Thermodynamics. Entropy 2014, 16, 3434-3470.

View more citation formats

Related Articles

Article Metrics

For more information on the journal, click here


Cited By

[Return to top]
Entropy EISSN 1099-4300 Published by MDPI AG, Basel, Switzerland RSS E-Mail Table of Contents Alert