We discuss properties of the "beamsplitter addition" operation, which provides a non-standard scaled convolution of random variables supported on the non-negative integers. We give a simple expression for the action of beamsplitter addition using generating functions. We use this to give a self-contained and purely classical proof of a heat equation and de Bruijn identity, satisfied when one of the variables is geometric.
It is argued that if the non-unitary measurement transition, as codified by Von Neumann, is a real physical process, then the "probability assumption" needed to derive the Second Law of Thermodynamics naturally enters at that point. The existence of a real, indeterministic physical process underlying the measurement transition would therefore provide an ontological basis for Boltzmann's Stosszahlansatz and thereby explain the unidirectional increase of entropy against a backdrop of otherwise time-reversible laws. It is noted that the Transactional Interpretation (TI) of quantum mechanics provides such a physical account of the non-unitary measurement transition, and TI is brought to bear in finding a physically complete, non-ad hoc grounding for the Second Law.
Remarkable progress of quantum information theory (QIT) allowed to formulate mathematical theorems for conditions that data-transmitting or data-processing occurs with a non-negative entropy gain. However, relation of these results formulated in terms of entropy gain in quantum channels to temporal evolution of real physical systems is not thoroughly understood. Here we build on the mathematical formalism provided by QIT to formulate the quantum H-theorem in terms of physical observables. We discuss the manifestation of the second law of thermodynamics in quantum physics and uncover special situations where the second law can be violated. We further demonstrate that the typical evolution of energy-isolated quantum systems occurs with non-diminishing entropy. 
Peter Woit has just made the final draft (dated 10/25/16) of his new textbook Quantum Theory, Groups and Representations: An Introduction freely available for download from his website. It covers quantum theory with a heavy emphasis on groups and representation theory and
“contains significant amounts of material not well-explained elsewhere.” He expects to finish up the diagrams and publish it next year some time, potentially through Springer.
Syndicated copies to:
Learn about quantum computation and quantum information in this advanced graduate level course from MIT.
Syndicated copies to:
About this course
Already know something about quantum mechanics, quantum bits and quantum logic gates, but want to design new quantum algorithms, and explore multi-party quantum protocols? This is the course for you!
In this advanced graduate physics course on quantum computation and quantum information, we will cover:
- The formalism of quantum errors (density matrices, operator sum representations)
- Quantum error correction codes (stabilizers, graph states)
- Fault-tolerant quantum computation (normalizers, Clifford group operations, the Gottesman-Knill Theorem)
- Models of quantum computation (teleportation, cluster, measurement-based)
- Quantum Fourier transform-based algorithms (factoring, simulation)
- Quantum communication (noiseless and noisy coding)
- Quantum protocols (games, communication complexity)
Research problem ideas are presented along the journey.
What you’ll learn
- Formalisms for describing errors in quantum states and systems
- Quantum error correction theory
- Fault-tolerant quantum procedure constructions
- Models of quantum computation beyond gates
- Structures of exponentially-fast quantum algorithms
- Multi-party quantum communication protocols
Meet the instructor
Isaac Chuang Professor of Electrical Engineering and Computer Science, and Professor of Physics MIT
Went on vacation or fell asleep at the internet wheel this week? Here’s some of the interesting stuff you missed.
Science & Math
- Context Specific and Differential Gene Co-expression Networks via Bayesian Biclustering | PLOS Computational Biology
- The Competing Incentives of Academic Research in Mathematics
- [1607.08473] Quantum circuits and low-degree polynomials over F_2
- This Physics Pioneer Walked Away from it All | Nautilus
- Monumental proof to torment mathematicians for years to come: Conference on Shinichi Mochizuki’s work inspires cautious optimism. | Nature
- What Your Brain Looks Like When It Solves a Math Problem | New York Times
- Habits of Highly Mathematical People
- Why You Should Care About High-Dimensional Sphere Packing | Roots of Unity
- Initial steps toward reproducible research
- Bridging the Curation Gap between Research and Libraries – A Case Study
- Quantum steampunk: Quantum information applied to thermodynamics
- How Vector Space Mathematics Reveals the Hidden Sexism in Language
- How Sound Can Make Food Taste Better | Nautilus
- Top 10 algorithms of 20th century numerical analysis, from a talk by Alex Townsend
- UK vs. US: Who’s got the right way to teach math(s)? | Math with Bad Drawin
- Physics & Caffeine: Stop Motion Film Uses a Cup of Coffee to Explain Key Co
- The Water Kingdom: A Secret History of China by Philip Ball (review)
- The master of them all: Book review for”Leonhard Euler: Mathematical Genius in the Enlightenment” | The Economist
- Biologists Search for New Model Organisms: The bulk of biological research is centered on a handful of species. Are we missing a huge chunk of life’s secrets?
- One-sentence proof of Fermat’s theorem on sums of two squares | Fermat’s Library
- This protein designer aims to revolutionize medicines and materials
- Our last common ancestor inhaled hydrogen from underwater volcanoes
- Meet Luca, The Ancestor of All Living Things | New York Times
- *Disconnected, fragmented, or united? a trans-disciplinary review of network
- What’s Behind A Science vs. Philosophy Fight? | Big Think
- What is a “Neutral Network” Anyway? An Exploration and Rediscovery of the Aims of Net Neutrality in Theory and Practice
- The Brachistochrone Curve: The Problem of Quickest Descent | Fermat’s Library
- In what sense is Quantum Mechanics a theory of information? | Quora
- Major transitions in information technology | Philosophical Transactions of
- Human brain mapped in unprecedented detail: Nearly 100 previously unidentified brain areas revealed by examination of the cerebral cortex. | Nature
- Cell biologists should specialize, not hybridize: Dry cell biologists, who bridge computer science and cell biology, should have a pivotal role in driving effective team science, says Assaf Zaritsky | Nature
- Internet 3.0: How we take back control from the giants | New Scientist
- How a Guy From a Montana Trailer Park Overturned 150 Years of Biology | The Atlantic
- People can sense single photons | Nature News & Comment
- Defining synergy thermodynamically using quantitative measurements of entropy and free energy
- A Prime Case of Chaos | AMS.org
- Murray Gell-Mann (video interviews) – YouTube
- Mathematics & Chalk: A teary goodbye to Hagomoro | Jeremy Kun
- Want to Change Academic Publishing? Just Say No | Chronicle
- Textbooks Show Aging Signs: Curated Guides Are Next – 10+ Disruptive Factors Transforming the World of Education and Learning — Consequences, Opportunities, Tools
- Simon & Schuster, Penguin, Random House Don’t Want to Talk About Their Ebook Sales
- Amazon Sales Rank: Taming the Algorithm | Self-Publishing Author Advice
- What Authors Should Know About Advance Review Copies
- Ingram Launches Ingram Academic Services
- How a Publishing House Designs a Book Cover
- How Indie Bookstores Help Drive Book Discoverability
- How to Grow Your Email List
- 3 Ways Indie Publishers Sell Books | Digital Book World
- 10 Self-Publishing Trends to Watch
- Ingram Launches Academic Services for University Presses and Academic Publishers
- Indigo Goes Where Amazon, B&N, Goodreads, and a Dozen Publishers and Startus Have Dared to Tread
- How To Make An Ebook Feel More Like A Real Book
- Looking for open digital collections – Wynken de Worde
Indieweb, Internet, Identity, Blogging, Social Media
- What is Open Source?
- Microformats with Tantek Çelik | tlks.io
- My Text Editor is Absolutely Sublime | Devon Zuegel
- My zsh aliases | Devon Zuegel
- XOXO Festival
- Web Design in 4 minutes
- Custom Elements
- Design Principles
- Infographic: The Optimal Length for Every Social Media Update
- Notes For New (and Potential) Twitter Followers | Whatever
- How Blogs Work Today – Whatever
- My reply to: How Blogs Work Today | Whatever
- Unicode Character ‘ZERO WIDTH SPACE’ (U 200B)
- A Book Apart, Practical SVG
- Gillmor Gang Trumpathon
- The best news aggregation service – The Sweet Setup
- Social Startup Sprinklr Is Now Valued At $1.8 Billion After $105 Million Raise | Forbes
- Epeus’ epigone: Digital publics, Conversations and Twitter
- The New Meaning of Success
- 7 Lessons from the Future of Content: Part One — Tools Are Cheap, Time Is Expensive
- 7 Lessons from the Future of Content: Part Two — Let’s Play Risk
- Aron Pilhofer Joining Temple University School of Media and Communication
- Secrets and agents: George Akerlof’s 1970 paper, “The Market for Lemons”, is a foundation stone of information economics. The first in our series on seminal economic ideas | The Economist
- John Oliver has the takedown of Donald Trump’s Republican convention
- Reference: New Interactive Map Of 100,000 Photos and Videos Reveal “Lost London in the Victorian Era”
- “better modifiers than “insane(ly)” (Grammar and Usage)
- A lesson in the errors of statistical thinking: Nate Silver on Trump
- Trump & Putin. Yes, It’s Really a Thing
- Charlie Parker Plays with Dizzy Gillespie in Only Footage Capturing the “Bird” in True Live Performance
- Let Me Remind You Fuckers Who I Am (Shit HRC Can’t Say/satire)
I’m already a major chunk of the way through the book, having had an early ebook version of the text prior to publication. This is the published first edition with all the diagrams which I wanted to have prior to finishing my full review, which is forthcoming.
One thing I will mention is that it’s got quite a bit more philosophy in it than most popular science books with such a physics bent. Those who aren’t already up to speed on the math and science of modern physics can certainly benefit from the book (like most popular science books of its stripe, it doesn’t have any equations — hairy or otherwise), and it’s certain to help many toward becoming members of both of C.P. Snow’s two cultures. It might not be the best place for mathematicians and physicists to start moving toward the humanities with the included philosophy as the philosophy is very light and spotty in places and the explanations of the portions they’re already aware of may put them out a bit.
I’m most interested to see how he views complexity and thinking in the final portion of the text.
More detail to come…Syndicated copies to:
Running a brain-twisting thought experiment for real shows that information is a physical thing – so can we now harness the most elusive entity in the cosmos?
This is a nice little overview article of some of the history of thermodynamics relating to information in physics and includes some recent physics advances as well. There are a few references to applications in biology at the micro level as well.
- Second Law of Thermodynamics with Discrete Quantum Feedback Control by Takahiro Sagawa and Masahito Ueda; Phys. Rev. Lett. 100, 080403 – Published 26 February 2008
- Work and information processing in a solvable model of Maxwell’s demon by Dibyendu Mandal and Christopher Jarzynski; PNAS vol. 109 no. 29, July 17, 2012
- Thermodynamic Costs of Information Processing in Sensory Adaptation by Pablo Sartori, Léo Granger, Chiu Fan Lee, and Jordan M. Horowitz; PLOS December 11, 2014 http://dx.doi.org.sci-hub.cc/10.1371/journal.pcbi.1003974
- Intermittent transcription dynamics for the rapid production of long transcripts of high fidelity by Depken M1, Parrondo JM, Grill SW; Cell Rep. 2013 Oct 31;5(2):521-30. doi: 10.1016/j.celrep.2013.09.007
- The stepping motor protein as a feedback control ratchet by Martin Bier; BioSystems 88 (2007) 301–307
In catching up on blogs/reading from the holidays, I’ve noticed that physicist Sean Carroll has a forthcoming book entitled The Big Picture: On the Origins of Life, Meaning, and the Universe Itself (Dutton, May 10, 2016) that will be of interest to many of our readers. One can already pre-order the book via Amazon.
Prior to the holidays Sean wrote a blogpost that contains a full overview table of contents, which will give everyone a stronger idea of its contents. For convenience I’ll excerpt it below.
I’ll post a review as soon as a copy arrives, but it looks like a strong new entry in the category of popular science books on information theory, biology and complexity as well as potentially the areas of evolution, the origin of life, and physics in general.
As a side bonus, for those reading this today (1/15/16), I’ll note that Carroll’s 12 part lecture series from The Great Courses The Higgs Boson and Beyond (The Learning Company, February 2015) is 80% off.
THE BIG PICTURE: ON THE ORIGINS OF LIFE, MEANING, AND THE UNIVERSE ITSELF
* Part One: Cosmos
- 1. The Fundamental Nature of Reality
- 2. Poetic Naturalism
- 3. The World Moves By Itself
- 4. What Determines What Will Happen Next?
- 5. Reasons Why
- 6. Our Universe
- 7. Time’s Arrow
- 8. Memories and Causes
* Part Two: Understanding
- 9. Learning About the World
- 10. Updating Our Knowledge
- 11. Is It Okay to Doubt Everything?
- 12. Reality Emerges
- 13. What Exists, and What Is Illusion?
- 14. Planets of Belief
- 15. Accepting Uncertainty
- 16. What Can We Know About the Universe Without Looking at It?
- 17. Who Am I?
- 18. Abducting God
* Part Three: Essence
- 19. How Much We Know
- 20. The Quantum Realm
- 21. Interpreting Quantum Mechanics
- 22. The Core Theory
- 23. The Stuff of Which We Are Made
- 24. The Effective Theory of the Everyday World
- 25. Why Does the Universe Exist?
- 26. Body and Soul
- 27. Death Is the End
* Part Four: Complexity
- 28. The Universe in a Cup of Coffee
- 29. Light and Life
- 30. Funneling Energy
- 31. Spontaneous Organization
- 32. The Origin and Purpose of Life
- 33. Evolution’s Bootstraps
- 34. Searching Through the Landscape
- 35. Emergent Purpose
- 36. Are We the Point?
* Part Five: Thinking
- 37. Crawling Into Consciousness
- 38. The Babbling Brain
- 39. What Thinks?
- 40. The Hard Problem
- 41. Zombies and Stories
- 42. Are Photons Conscious?
- 43. What Acts on What?
- 44. Freedom to Choose
* Part Six: Caring
- 45. Three Billion Heartbeats
- 46. What Is and What Ought to Be
- 47. Rules and Consequences
- 48. Constructing Goodness
- 49. Listening to the World
- 50. Existential Therapy
- Appendix: The Equation Underlying You and Me
- Further Reading
Springer recently announced the publication of the book Quantum Biological Information Theory by Ivan B. Djordjevic, in which I’m sure many readers here will have interest. I hope to have a review of it shortly after I’ve gotten a copy. Until then…
From the publisher’s website:
This book is a self-contained, tutorial-based introduction to quantum information theory and quantum biology. It serves as a single-source reference to the topic for researchers in bioengineering, communications engineering, electrical engineering, applied mathematics, biology, computer science, and physics. The book provides all the essential principles of the quantum biological information theory required to describe the quantum information transfer from DNA to proteins, the sources of genetic noise and genetic errors as well as their effects.
- Integrates quantum information and quantum biology concepts;
- Assumes only knowledge of basic concepts of vector algebra at undergraduate level;
- Provides a thorough introduction to basic concepts of quantum information processing, quantum information theory, and quantum biology;
- Includes in-depth discussion of the quantum biological channel modelling, quantum biological channel capacity calculation, quantum models of aging, quantum models of evolution, quantum models on tumor and cancer development, quantum modeling of bird navigation compass, quantum aspects of photosynthesis, quantum biological error correction.
Springer also has a downloadable copy of the preface and a relatively extensive table of contents for those looking for a preview. Dr. Djordjevic has been added to the ever growing list of researchers doing work at the intersection of information theory and biology.Syndicated copies to:
Yesterday, via a notification from Lanyard, I came across a notice for the upcoming conference “The Information Universe” which hits several of the sweet spots for areas involving information theory, physics, the origin of life, complexity, computer science, and microbiology. It is scheduled to occur from October 7-9, 2015 at the Infoversum Theater in Groningen, The Netherlands.
I’ll let their site speak for itself below, but they already have an interesting line up of speakers including:
- Erik Verlinde, Professor Theoretical Physics, University of Amsterdam, Netherlands
- Alex Szalay, Alumni Centennial Professor of Astronomy, The Johns Hopkins University, USA
- Gerard ‘t Hooft, Professor Theoretical Physics, University of Utrecht, Netherlands
- Gregory Chaitin, Professor Mathematics and Computer Science, Federal University of Rio de Janeiro, Brasil
- Charley Lineweaver, Professor Astronomy and Astrophysics, Australian National University, Australia
- Lude Franke, Professor System Genetics, University Medical Center Groningen, Netherlands
Conference synopsis from their homepage:
Four decades ago, Stephen Hawking posed the black hole information paradox about black holes and quantum theory. It still challenges the imaginations of theoretical physicists today. Yesterday, Amanda Peet (University of Toronto) presented the a lecture entitled “String Theory Legos for Black Holes” yesterday at the Perimeter Institute for Theoretical Physics. A quick overview/teaser trailer for the lecture follows along with some additional information and the video of the lecture itself.
The “Information Paradox” with Amanda Peet (teaser trailer)
“Black holes are the ‘thought experiment’ par excellence, where the big three of physics – quantum mechanics, general relativity and thermodynamics – meet and fight it out, dragging in brash newcomers such as information theory and strings for support. Though a unification of gravity and quantum field theory still evades string theorists, many of the mathematical tools and ideas they have developed find applications elsewhere.
One of the most promising approaches to resolving the “information paradox” (the notion that nothing, not even information itself, survives beyond a black hole’s point-of-no-return event horizon) is string theory, a part of modern physics that has wiggled its way into the popular consciousness.
On May 6, 2015, Dr. Amanda Peet, a physicist at the University of Toronto, will describe how the string toolbox allows study of the extreme physics of black holes in new and fruitful ways. Dr. Peet will unpack that toolbox to reveal the versatility of strings and (mem)branes, and will explore the intriguing notion that the world may be a hologram.
Amanda Peet is an Associate Professor of Physics at the University of Toronto. She grew up in the South Pacific island nation of Aotearoa/New Zealand, and earned a B.Sc.(Hons) from the University of Canterbury in NZ and a Ph.D. from Stanford University in the USA. Her awards include a Radcliffe Fellowship from Harvard and an Alfred P. Sloan Foundation Research Fellowship. She was one of the string theorists interviewed in the three-part NOVA PBS TV documentary “Elegant Universe”.
Web site: http://ap.io/home/.