I am wondering about the use of the so-called quantum thermodynamics and its theoretical advantage: can quantum machines outperform the classical analogues (supposing of course the absolute temperature is NOT zero)?

  • $\begingroup$ What is meant by "outperform"? $\endgroup$ – Daddy Kropotkin Jan 17 '19 at 19:49

tl;dr: The main theoretical advantage of quantum thermodynamics is that it describes systems that classical thermodynamics just can't describe.

You ask whether quantum thermodynamics is or will be better than classical thermodynamics. This seems to be similar to the question whether quantum computation can be better than classical computation - but sadly, I don't think it is.

Classical thermodynamics only works for large systems with a large number of degrees of freedom. It is just not applicable on small scales. The central definitions of thermodynamics such as "work" or "temperature" are fuzzy at best in small systems with only a few degrees of freedom.

Quantum thermodynamics is just a new theory that (often) tries to describe small systems with only a few degrees of freedom in terms that relate to classical thermodynamics.

Thus you can't really compare the two as they work in different realms, although quantum thermodynamics should condense to classical thermodynamics for large systems. Some authors find quantum systems that seem to "outperform" classical systems, but this is nonsensical, because classical thermodynamics just doesn't apply. They only "outperform" if you make a few assumptions about how thermodynamics could be extended to small systems.

But then, why quantum thermodynamics? For many reasons, for instance:

  1. How does it emerge? In particular: Quantum processes are ultimately reversible, classical thermodynamics has mainly irreversible processes. How do those come about?
  2. We increasingly need knowledge of thermodynamics at small scales (think of computer systems for instance). Although there are other tools to investigate these problems, the language and tools from thermodynamics are nice to have, so we'd like to apply them at these scales, too.
  3. Despite the huge success of equilibrium thermodynamics, non-equilibrium thermodynamics still offers plenty of open questions. In contrast to classical thermodynamics, you'll find a lot of quantum thermodynamics papers talking about dynamics. For instance, people like to study thermalization (the process towards equilibrium) a lot. This is just simpler in small systems than it is in large systems.
  4. A lot of quantum thermodynamics actually describes open quantum systems which are studied on their own for various good reasons. People discovered that the classical language of thermodynamics provides a different view so that you can reinterpret certain results and work out different problems that can eventually help to understand open quantum systems better.

And these are just some reasons. Naturally, when a field is very young, there are a lot of "low hanging fruit" which attracts a lot of people and creates a lot of results, not all of which are sound.


To answer your question I must first clarify some ideas!

Engines transform some form of energy, such as thermal, chemical, mechanical, or electrical energy into useful work. Their efficiency, namely, the ratio of the output work to the input energy, is restricted to 1 at most by energy conservation. Engines converting mechanical energy into work may, in principle, approach unit efficiency. By contrast, the efficiency of heat-to-work conversion in a cyclic heat engine that operates between cold and hot thermal baths is independent of the specific design and limited by the universal Carnot bound. This bound follows from the second law of thermodynamics under the reversibility condition. Over the past two decades, extensive studies of thermal machines in the quantum domain have sought to reveal either fundamentally new aspects of thermodynamics or unique quantum advantages compared to their classical counterparts. The study has shown a remarkable similarity with macroscopic thermodynamical results, thus raising the issue of what is quantum in quantum thermodynamics.

What we have seen is that quantum thermodynamic machines do not rely on quantumness or they are truly quantum, exhibit "quantum advantage" but do not contradict the second law of thermodynamics. By "quantum advantage" I want to mean that some results are the thermodynamical equivalence of all engine types in the quantum regime of small action with respect to Planck’s constant. They have the same power, the same heat, and the same efficiency, and they even have the same relaxation rates and relaxation modes.

Yet, despite the great progress achieved, both theoretically and experimentally, the potential of quantum thermal machines for useful quantum technology applications only begins to unfold.


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