I spy with my little eye…something algebraic.

Look at this picture.

Peter 1

Does any part of it surprise you? Look more closely.

Peter 2

Now? Try crossing your eyes.

Peter 3

Do you see a boy’s name?

I spell “Peter” with two e’s, but “Piotr” and “Pyotr” appear as authors’ names in papers’ headers. Finding “Petr” in a paper shouldn’t have startled me. But how often does “Gretchen” or “Amadeus” materialize in an equation?

When I was little, my reading list included Eye Spy, Where’s Waldo?, and Puzzle Castle. The books teach children to pay attention, notice details, and evaluate ambiguities.

That’s what physicists do. The first time I saw the picture above, I saw a variation on “Peter.” I was reading (when do I not?) about the intersection of quantum information and thermodynamics. The authors were discussing heat and algebra, not saints or boys who picked pecks of pickled peppers. So I looked more closely.

Each letter resolved into part of a story about a physical system. The P represents a projector. A projector is a mathematical object that narrows one’s focus to a particular space, as blinders on a horse do. The E tells us which space to focus on: a space associated with an amount E of energy, like a country associated with a GDP of $500 billion.

Some of the energy E belongs to a heat reservoir. We know so because “reservoir” begins with r, and R appears in the picture. A heat reservoir is a system, like a colossal bathtub, whose temperature remains constant. The Greek letter \tau, pronounced “tau,” represents the reservoir’s state. The reservoir occupies an equilibrium state: The bath’s large-scale properties—its average energy, volume, etc.—remain constant. Never mind about jacuzzis.

Piecing together the letters, we interpret the picture as follows: Imagine a vast, constant-temperature bathtub (R). Suppose we shut the tap long enough ago that the water in the tub has calmed (\tau). Suppose the tub neighbors a smaller system—say, a glass of Perrier.* Imagine measuring how much energy the bath-and-Perrier composite contains (P). Our measurement device reports the number E.

Quite a story to pack into five letters. Didn’t Peter deserve a second glance?

The equation’s right-hand side forms another story. I haven’t seen Peters on that side, nor Poseidons nor Gallahads. But look closely, and you will find a story.

 

The images above appear in “Fundamental limitations for quantum and nanoscale thermodynamics,” published by Michał Horodecki and Jonathan Oppenheim in Nature Communications in 2013.

 

*Experts: The ρS that appears in the first two images represents the smaller system. The tensor product represents the reservoir-and-smaller-system composite.

This entry was posted in Reflections, Theoretical highlights and tagged , , , , by Nicole Yunger Halpern. Bookmark the permalink.

About Nicole Yunger Halpern

I recently completed a physics PhD with the buccaneers of Quantum Frontiers. Starting in Sept. 2018, I'll work as an ITAMP Postdoctoral Fellow at the Harvard-Smithsonian Institute for Theoretical Atomic, Molecular, and Optical Physics (ITAMP). You'll be able to catch me at ITAMP, in Harvard's physics department, or at MIT. My research consists of what I like to call "quantum steampunk": I combine quantum information with thermodynamics, contributing to the theory of quantum thermodynamics and applying quantum thermodynamics across science. Before beginning my PhD at Caltech, I studied at Dartmouth College and the Perimeter Institute for Theoretical Physics. I like my quantum information physical, my math algebraic, and my spins rotated but not stirred.

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