Identifying in the second law of thermodynamics the logical foundation of physical theories

Arthur Eddington once famously wrote: “If your theory is found to be against the second law of thermodynamics, […] there is nothing for it but to collapse in deepest humiliation.” So why not take the second law as an axiom, on which physical theories are built, rather than as a consequence to be tested? The problem is that, in its conventional thermodynamic formulation, the second law relies on quite a lot of physics to have been already introduced, and it is not clear how one could assume its validity before other concepts like “work” or “heat” are even defined.

In a paper published today on Physical Review Research, we identify in von Neumann’s information engine the conceptual device that allows us to discuss the second law already from the early stages of the construction of a physical theory, when its most fundamental logical structures are being laid down. What we find is that, by concatenating two information engines in a closed cycle, the second law can be thought of as the requirement that no information can be created from nothing, thus guaranteeing the internal logical consistency of the theory.

All work and no play makes Maxwell’s demon tired

From the popular summary of my paper with Arshag and Mark, “Thermodynamic constraints on quantum information gain and error correction” just published on PRX Quantum.

It is now widely accepted that Maxwell’s demon does not, in fact, break the second law of thermodynamics, if the energetic cost of resetting its memory is taken into account. This resolution of the paradox is known as Landauer’s principle.

Landauer’s principle is only the limiting case of a more general triple trade-off relation between the thermodynamic, information-theoretic, and logic performances of the demon.

In this work, we delve into the inner workings of Maxwell’s demon by considering how it behaves in the quantum error correction setting. We show that Landauer’s principle is only the limiting case of a more general triple trade-off relation between the thermodynamic, information-theoretic, and logic performances of the demon. For example, we show that for most measurements that the demon can perform, extracting work above the Carnot limit is penalized by a drop in the error correction fidelity. Moreover, when the demon successfully performs perfect error correction, work extraction above the Carnot limit becomes impossible with most quantum measurements. Finally, we realize that the amount of information that the demon can extract about the error type is bounded from above by the dissipated heat during that process. Interestingly, this also gives physical meaning to negative values of this information gain.

The meaning of “Quantum Quia”

I take the opportunity of the 700th anniversary of Dante‘s death to explain the meaning of this blog’s name.

Illustration by Gustave Doré.

In Dante’s Purgatorio, Canto III, Virgil warns Dante about the limits of human intellect, which is able to understand and describe relations between events (the quia, Latin for “because/for”), but not the events’ “true reality”.

Fast forward to the 21st century, I believe that this viewpoint is close in spirit to the idea, which I’m very fond of at present, that the deepest laws of physics tell us more about our “learning mechanisms” than they do about “reality” (whatever that means).

Here is the excerpt from Dante’s Purgatorio, Canto III, verses 37-45:

“State contenti, umana gente, al quia,
che se possuto aveste vedere tutto
mestier non era parturir Maria;
e disiar vedeste sanza frutto
tai che sarebbe lor disio quetato,
ch’etternalmente è dato lor per lutto:
io dico d’Aristotile e di Plato
e di molt’altri”; e qui chinò la fronte,
e più non disse, e rimase turbato.

The same excerpt in English:

“Mortals, remain contented at the quia;
For if ye had been able to see all,
No need there were for Mary to give birth;
And ye have seen desiring without fruit,
Those whose desire would have been quieted,
Which evermore is given them for a grief.
I speak of Aristotle and of Plato,
And many others;” and here bowed his head,
And more he said not, and remained disturbed.

Postdoc position available

Position title and duration: postdoc or research assistant professor, depending on the candidate’s qualifications. The appointment is offered initially for a one-year period, with the possibility of further extensions up to three years of total duration.

Description: this position is offered by the Quantum Information Theory Group within the collaboration “Extreme Universe”, headed by Prof. Tadashi Takayanagi (YITP, Kyoto University). This collaboration brings together Japan-based world-renowned researchers in quantum information theory, quantum gravity, cosmology, and condensed matter physics, with the aim of creating new and exciting bridges between these very active areas of research. The successful candidate will work in close contact with Prof. Francesco Buscemi (Nagoya University), but is expected to interact also with the rest of the collaboration group and to participate in various interdisciplinary meetings within the project. The successful candidate is expected to commence their appointment on April 2022 or as soon as possible after that.

Requirements: applicants are expected to hold a PhD degree in a theoretical field related to quantum information sciences by the time they begin their appointment. Ideally, they will be familiar with recent ideas and techniques in quantum information theory and have at the same time strong interests in fundamental questions in theoretical physics.

Submission procedure: interested candidates should provide

  1. a cover letter;
  2. an up-to-date curriculum vitae;
  3. a research statement;
  4. an up-to-date list of research achievements (including published papers, preprints, talks, posters, etc.);
  5. contact information of three references able to provide recommendation letters upon request.

The application can be done by sending the above documents directly to or through the project’s webpage at (where also other openings are advertised)

Submission deadline: 30 November 2021

For further inquiries, please contact me at

No Hamiltonian? No time-reversal! Only retrodiction.

Is there an observer-independent time-reversal in physics? Only for Hamiltonian dynamics, we argue. Otherwise there’s only retrodiction, which of course depends on the retrodictor’s (prior) believes. The paper (co-authored with Clive C. Aw and Valerio Scarani) is freely available from AVS Quantum Science website, where it is highlighted as a Featured Article. Below is a talk I recently gave on these ideas.

Overview on the Petz transpose map

I was recently invited to give an overview talk on Petz’s “transpose” or “recovery” map at the workshop Workshop on Quantum Information and Quantum Black Holes, organized by Norihiro Iizuka (Osaka) and Tomonori Ugajin (Kyoto). I’ve put together what I came to learn about the properties of Petz’s transpose map, its uses is various areas of information theory and physics, and (most importantly!) its conceptual meaning. Slides are available here. Mark Wilde’s textbook contains a chapter entirely devoted to the technical aspects of Petz’s map and the theory of approximate recoverability.

Fugue in D Minor for four voices (subject by Gedalge)

I wrote this while preparing for the Eighth Year Exam of Classical Composition at the Conservatory of Milan, in 1999 (or perhaps 2000?). The subject (the first four bars) is one of Gedalge’s classical treatise’s exercises (it’s the number 4). I remember it was really a pleasure to see a fugue getting together nicely, and this is one of the best I wrote. (My countersubject, in particular, functions very well…)

I am jealously preserving all my handwritten scores, but recently I also found a transcription I made in Finale (I believe that was the 1998 version; a real pain to use) and here is its MIDI rendition: enjoy! 🙂