Quantum Physics: An Information Theory
A special issue of Entropy (ISSN 1099-4300). This special issue belongs to the section "Quantum Information".
Deadline for manuscript submissions: 31 March 2026 | Viewed by 15
Special Issue Editor
Special Issue Information
Dear Colleagues,
The concept of entropy was first introduced by Rudolf Clausius in 1865. He coined the term entropy—derived from the Greek word for “transformation”—to describe the inherent irreversibility of natural processes in thermodynamics. Following the pioneering work of Ludwig Boltzmann in 1872, the general expression for thermodynamic entropy was later formalized as the Gibbs entropy:
 |
(1) |
where kB is the Boltzmann constant, and pi is the probability of a microstate.
In 1948, Claude Shannon introduced the concept of information entropy, establishing the foundations of information theory. Shannon’s entropy takes the same mathematical form as Gibbs entropy, i.e., Equation (1) with kB = 1, logarithms typically taken in base 2 (for units of bits), and pi representing the probability of a discrete event i.
According to E.T. Jaynes (1957), thermodynamic entropy—as formulated in statistical mechanics via the Gibbs entropy—can be understood as an application of Shannon’s information theory. In this perspective, entropy quantifies an uncertainty or lack of information about the microscopic state of a system. In relation to this view, Landauer’s principle sets a thermodynamic limit on the minimum amount of heat that must be dissipated when processing information. How physics and information theory are related extends deeper with the advent of quantum physics.
Quantum theory, which governs the microscopic realm, associates a probability distribution with each observable of a quantum state. Is there an entropy intrinsically associated with a quantum state, that is independent of the choice of observable? This question was affirmatively addressed by D. Geiger and Z. Kedem (2021), who proposed a definition of quantum entropy for pure states in phase space. Their formulation satisfies several invariance properties, including invariance under canonical transformations, Lorentz transformations (relativity), and charge–parity–time (CPT) symmetry transformations. They also hypothesized that such an entropy production cannot decrease for a closed quantum system (since information cannot be gained), therefore advocating for an arrow of time. The analog of the third law of thermodynamics applied to the Geiger–Kedem entropy is the well-known entropic uncertainty principle first articulated by R. Leipnik in 1959. Unlike classical thermodynamic entropy, this quantum entropy is intrinsic to the pure quantum state, rather than emerging from ignorance or ensemble mixtures. Other forms of the so-called quasi-entropy, such as Wehrl entropy based on quasi-probability distributions, have also been explored in the past.
A distinct and widely used formulation of quantum entropy was introduced by John von Neumann in 1927:
 |
(2) |
where ρ is the density matrix of the quantum mechanical system and Tr denotes the trace. The von Neumann entropy quantifies the classical uncertainty associated with a mixed quantum state, i.e., a statistical mixture of pure states. Notably, it vanishes for pure states. Numerous attempts have been made to connect von Neumann entropy with thermodynamic entropy.
The concept of quantum thermalization, introduced by M. Srednicki in 1994, demonstrates—under Berry’s conjecture—a link between quantum theory and thermodynamics. More recently, A. Schlatter and R.E. Kastner (2024) linked Landauer’s principle to the Geiger–Kedem entropy production during photon absorption. Together, these advances strengthen the conceptual bridge between quantum physics and classical thermodynamics. We highlight the pioneer work of A. Zeilinger, J. Clauser, A. Aspect, J. Preskill, D. Deutsch, and B. Terhalon in quantum physics, particularly in the realms of information theory and quantum computing.
This Special Issue invites researchers to address this exciting field of interconnection between quantum physics and information theory with the emergence of thermodynamics. Topics of interest include, but are not limited to, the following:
- Does quantum entropy play a physical role?
- What are the exact connections between quantum entropy and thermodynamics entropy?
- Quantum thermalization.
- Evaluation of quantum entropy production in physical scenarios (atomic physics, cavity constructions, particle collisions, scattering, and the arrow of time). Is the Geiger–Kedem hypothesis, i.e., their entropy never decreases in a closed system, verified or falsified?
- Gravity, general relativity, and entropy production.
- Black hole entropy.
- Physics as information science.
- Quantum computing; in particular, the role of quantum entropy in achieving a better understanding of the quantum computing gates and processes.
Dr. Davi Geiger
Guest Editor
Manuscript Submission Information
Manuscripts should be submitted online at www.mdpi.com by registering and logging in to this website. Once you are registered, click here to go to the submission form. Manuscripts can be submitted until the deadline. All submissions that pass pre-check are peer-reviewed. Accepted papers will be published continuously in the journal (as soon as accepted) and will be listed together on the special issue website. Research articles, review articles as well as short communications are invited. For planned papers, a title and short abstract (about 100 words) can be sent to the Editorial Office for announcement on this website.
Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere (except conference proceedings papers). All manuscripts are thoroughly refereed through a single-blind peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Entropy is an international peer-reviewed open access monthly journal published by MDPI.
Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 2600 CHF (Swiss Francs). Submitted papers should be well formatted and use good English. Authors may use MDPI's English editing service prior to publication or during author revisions.
Keywords
- Gibbs entropy
- thermodynamic entropy
- quantum entropy
- quantum thermalization
- black hole entropy
Benefits of Publishing in a Special Issue
- Ease of navigation: Grouping papers by topic helps scholars navigate broad scope journals more efficiently.
- Greater discoverability: Special Issues support the reach and impact of scientific research. Articles in Special Issues are more discoverable and cited more frequently.
- Expansion of research network: Special Issues facilitate connections among authors, fostering scientific collaborations.
- External promotion: Articles in Special Issues are often promoted through the journal's social media, increasing their visibility.
- Reprint: MDPI Books provides the opportunity to republish successful Special Issues in book format, both online and in print.
Further information on MDPI's Special Issue policies can be found here.
