Eigenstate Localization

On being tired

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EIGENSTATE LOCALIZATION

Whether physics allows for the existence of systems that never relax is controversial.

Canonically, any system that starts off ordered into some specific, well-defined structure must, if left to its own devices, relax into a more even state and a state where it is all mixed up. This is a consequence of the second law of thermodynamics, the one that tells you that entropy, which is a measure of disorder, must always increase as time goes on. In fact, physicists often define time in terms of increasing entropy - if one state of some system is more disordered than another state of that same system, it is likely that the messier one occurred later in its lifetime. Without some external intervention, some omnipotent orderer who could keep everything just so, a state of high order will almost always be in the system’s past, and a less constrained, more relaxed one will lie in its future. 

You don’t have to know the second law of thermodynamics to understand this. Consider shaking a jar of colored sprinkles. Chances are you have never put the shaken jar down and found the sprinkles settling into neat layers of each color, instead of being all mixed up. If you were to come across a jar of sprinkles ordered by color, you would probably assume that it is newly bought, pristine, in the early days of its existence in someone’s kitchen. Its future? Definitely mixed. Ordering sprinkles after the jar has been shaken would require intervention and work instead of happening spontaneously, and a physicist would tell you that this is because the most mixed state has the highest entropy - and nature pushes systems towards that.

An awful lot of physics is built upon the second law, including how many heat engines and turbines that we still use operate, but its origin story is itself somewhat shaky. It is an empirical law, one that physicists did not derive mathematically but rather just have not yet found a system that truly contradicts it. And it also has roots in statistics where an argument that rests on counting and calculating probabilities seems to produce it even if the statistician tasked with the calculation knows absolutely nothing about physics. 

Statistically, the state with the highest entropy is simply one where the system has the highest number of equally likely states. And these states look messy only because any rigid, ordered structure changes the probability calculation. In the sprinkle example, if all red sprinkles are in one layer and all green in another layer then finding a green sprinkle in the red layer has an extremely low probability while finding a red sprinkle in the red layer has an extremely high probability. When they are all mixed up - and the entropy of the jar is very high - the probability of finding any color sprinkle in any part of the jar is roughly the same. This is the statistical argument in favor of the second law, a system is simply more likely to be in a state where many options are equally probable for it.

The process by which physical systems, like the sprinkle jar, relax is called thermalisation and until the 1950s physicists largely believed that unless you make a conscious effort to stop it, thermalisation will just always happen. Any system will always relax. Any structure will always dissolve or crumble. Any pattern will become like fuzzy pixelated static on old TVs. In 1958, however, Phill Anderson at AT&T Bell Labs in New Jersey published a paper that offered a counterexample. 

Today, this paper is universally accepted as correct and the quantum effects that Anderson  identified as being able to suppress thermalisation, and induce something called localization instead, have become part of contemporary physics canon. But his analysis only applied to a specific system akin to an infinitely thin wire and this specificity opened a myriad of new issues. Namely, how far could his argument be generalized? How many systems that never relax, that always hold onto some strict sense of order, some structure that will just not budge even if you wait as long as the lifetime of the universe, can actually exist?

In October, I reported an article about one effort to answer that question. “The situation kind of got stuck,” one researcher told me over Zoom as I tried my best to keep my jaw and shoulders relaxed, to hide how much the spectre of my to-do list was ordering my body to stay tense and alert. I asked him if he expected resolution anytime soon, but he seemed pretty uncomfortable with taking on the future like that.

Janine Antoni, “Mortar and Pestle.” 1999

“She’s so cool, I want her to come and chew on something in my house,” I turned and whispered to my best friend as we were watching the artist Janine Antoni discuss her body of work, much of which seemed to involve chewing, spitting or licking. We were watching her because Antoni’s discussion was part of an event that also included readings from local writers and I was lucky enough to be one of them. As the artist described chewing on a giant cube of chocolate then spitting some of it and molding it into chocolate boxes and tubes shaped and painted like lipstick, my heart was still pounding. I’ve given plenty of academic talks and lectures in my past life as a scientist, and I’ve sat on panels as a journalist, even interviewed some CEOs, but I’d never before read any of my more personal writing, the kind where “I” exists explicitly instead of just being implied. It had always been nerve-wracking enough to try and say something true about the nature of atoms to a room of people, but now those atoms were also the ones that made me up.

Antoni moved on to describe how she took a photograph of her tongue licking a partner’s eyeball, and I both calmed and quieted down some. I was really taken by her work, especially for how visceral and embodied it seemed to be and how many of her works seemed to require lots and lots of time. In many of the pieces that she discussed, she used her body as a tool or a reference, often accelerating an object's march towards a state of higher entropy through the fully universal tools of spit or touch. In one piece she invited a spider to weave a web on her body, a process that would have never worked without time and patience. As Antoni moved through her archive I found myself wistful for this kind of life, one where art is not rushed, where it can happen at the pace of bodies and nature, and where it can be visceral and messy. A high entropy life, so to speak.

The whole afternoon felt like a trip to a different type of existence. There were writers whom I admire and writers whose lists of accolades made me feel incredibly humbled. There was gorgeous and meaningful artwork. More artists spoke and blew me away with their own ways of processing the world. There was lots of laughter and kindness and inspiration. I almost couldn’t believe that I belonged there. A romanticized version of a writer’s life flashed before my eyes and when it ended, I couldn’t fully convince myself to dismiss the glimmers it left behind, even though I know how un-romantically most working writers live.

The piece I read was one of the shortest I’d written in a long time, but also one that I put a lot of time into, editing every line over and over, and reading it to my partner and my best friend after every tiny tweak. The process felt indulgent in its prolonged and iterative nature, but also deeply enjoyable, a delicious lingering on every word. It was the opposite of my day job on the news desk of a weekly magazine where words do really matter but deadlines loom above all. I was a different person when I was writing this piece than I am when I am at my desk. A calmer person maybe. A more relaxed one even.

One day after the event, my partner and I were at the New York Film Festival, at a screening of Luca Guadagnino’s Queer and I nearly lost my mind when the director himself as well as the two leads and the costume designer for the film walked out on the stage to introduce it. It was a fairly late screening, but we still decided to grab a drink afterwards and rehash our thoughts. Queer is an adaptation of a William S. Burroughs novel so it is psychedelic and impressionistic and has that veneer of grimy weirdness that either makes you really obsessed or really puts you off. My partner and I, two kids who once loved punk and heavy metal then shocked everyone by going to graduate school to become scientists, have always shared aesthetic affinities that overlap with just this flavor of artistic flair so the somewhat imperfect movie still really worked for us. We settled in a bar in Manhattan and discussed it over gin-and-tonics. 

Maybe it was the gin, but as we talked, I could feel the self-consciousness that usually keeps my body tense, the one that has me trying to compress myself into a ball, melt away. Slight bitterness of lime lingering on my tongue, my partner’s hand on my knee, and a daring thought: what if this is a life that I am allowed to live? A life where art and movies and being recognized as an artist myself are allowed, where they make sense, where there is nothing unusual about indulging in the aesthetic or simply finding time to think through the world in whatever shape that thinking takes. Not a fancy life, but one where creativity and relaxation do not feel like a commodity. Not an affluent life, but one where work does not rule all.

The answer to this question slapped me in the face the next day. I woke up just a little past my alarm and barely made it to the office on time, rushing through my morning routine to catch the train in an embarrassing subway platform sprint and settling at my desk just in time to look semi-respectable for an important person who was visiting from a different branch of the business. My weekend of art and relaxation immediately gave way to article quotas, meetings, interviews and interview prep, deadlines, Slack messages, subpar office cafeteria coffee in copious quantities, and intricate calculus of how much time I can actually spare to eat lunch. At the end of the day, I sat by the important person at the mandatory team dinner and finally confronted the fact that I had probably over-romanticized it all. 

Was the chatter in between readings at the event not full of rent and broker fee worries? Didn’t one of the artists directly speak about costs and demands on childcare? Even the artists and writers who don’t have to rush into the office day after day are tired and financially stressed, I thought, filling my mouth with spicy tofu, hoping that its flavor, rich in garlic and peppercorns, would keep me from looking exasperated. By the time I swallowed, someone prompted us all to go around the table and say what we love about our jobs. I reached for more tofu. A few hours later, in the blue glow of the computer screen in my home office, working on the manuscript for my first book, my eyes were watering and I tried really hard to solely blame that on the peppercorns. 

***

“Workers today are compelled to build a future that will exclude and marginalize them, designed by and for the benefit of their bosses,” write the editors of The World After Amazon in the book’s introduction. It collects science and speculative stories written by Amazon workers over the course of a year-long workshop initiated as Worker as Futurist Project. The editors go on to say:

“In our individualist, capitalist society, where the author and the artist are held up (deceptively) as the icons of unalienated labor and imaginative freedom, we should not underestimate how much dignity workers reclaim when they recognize themselves as creative writers. Dignity here stems from the idea that a worker deserves to imagine the future and have that vision matter.”

In the case of Amazon, specifically, this is a potent statement because its founder, Jeff Bezos, is a self-reported superfan of science fiction and has spoken about drawing inspiration for his companies from that fandom. With his forays into space exploration, he positions himself as part of the lineage of fictional heroes from novels and TV shows about traveling the universe while the people on his payroll experience the more dystopian side of science fiction, one where robots set the pace of their work in warehouses rather than one where they can dream about visiting the stars.

I attended the New York City book launch event for The World After Amazon and though I was there mostly by accident (a friend lives near the indie bookstore that hosted it), found myself furiously taking notes as one of the editors and some of the local organizers working to unionize Amazon spoke about the project and the company. I wrote down: “The world Amazon imagines only allows creativity to the few,”  and “Most words are published, printed or hosted by Amazon… are we all in some sense working for Amazon?” and “Amazon is envisioning a world where everyone is an entrepreneur or a consumer, no one is a worker, everyone is participating in capitalism within Amazon’s walled garden.” 

It’s not that I didn’t know how bad working conditions in Amazon’s warehouses are or how ever present the company is even if you boycott its delivery and grocery services - I’m lucky to move in social circles where this is a point of frequent discussion - but the notion of how it all connects to a specific vision of the future had not coalesced for me before. It is a future where you are either too tired and too overworked to imagine the future, or you have imagined something that you hope to sell to or through Amazon. One of the speakers at the book launch framed this in a poignant way: it’s a future where there are no workers, just budding entrepreneurs whose business is selling the physical might of their bodies. Here, the dream of commerce eats up all other dreams, and the only voice a person has speaks in the language of commodities. 

In a world where more than 40% of Americans adults want to be influencers and where all hobbies seem to be slated to eventually become side hustles and small businesses, this scenario is not that far-fetched and Amazon is not the sole culprit. But its size and ubiquity underscore the trend. As does its brutality to its workers who get injured at exceptionally high rates and often burn out of their jobs so quickly that the company can barely replace them. For those people, Amazon’s future is already here and selling their labor to the company has made them just another fungible, impersonal part of the system. 

In a discussion of her book Ashes: Grief and Revolution in a World on Fire on the Death Panel podcast, journalist Sarah Jaffe asserts that treating workers as just another interchangeable piece of a larger machine is just “what the system does.” She continues:

“It does not want us to…be humans with needs and wants and loves and idiosyncratic, weird little quirks that we all have and connections to other humans, right? Which is where the grief comes in. [The system] wants us to just be cogs in the machine and in any moment when we can find ways to not be a cog in that machine, those are [moments] where the possibilities for resistance are, right? Those are the cracks in the system that we can shove some roots into and try to grow [resistance].”

Being able to grieve is a complement to being able to imagine. The predecessor of grief is a conviction that something, or someone, matters. The first story in The World After Amazon is filled with grief. It follows a human-robot couple who once led an uprising against an Amazon-like entity that has swallowed most of society in the future. The two are reminiscing of how it all started and how the aftermath of their struggle was not without sacrifices and loss. And they are reminiscing in the face of impending loss too. The robot’s circuitry is failing and he will soon malfunction and stop remembering. 

In the book’s introduction as well as editor’s reflections on the project, the team behind Worker as Futurist Project acknowledge that most of the stories that Amazon employees wrote had a dystopian bend. This may reflect their lived experience of being exploited, or maybe be a function purely of pattern recognition where repeated instances of a better future not actually being better start to feel like a rule of nature. Reading through the book, I also wondered whether dealing with the prospect of grief through writing may be a necessary part of reclaiming dignity, of asserting that who you are and want does matter. As Jaffe suggests, feelings of grief, discontent, sometimes even despair are where resistance often begins. Before you start resisting, you may let them leave your body and land on the page.

Reading The World After Amazon invited me to think about both my writing and my feelings of powerlessness around the way I work. My first instinct was to feel lucky, lucky to have a job that is not immediately physically punishing and that does pay the rent. Being intellectually drained and feeling oppressed by deadlines is, in the grand scheme of things, a more manageable problem than many, I reminded myself. Though the rise of AI may soon set the pace of my work as a journalist in a way similar to robots setting the pace of work in warehouses, I am still afforded something like a voice. This is significant, and it does make my sense of personhood feel more secure. 

This is a perspective that I need so I can keep going every day, not as a reminder that it could be worse but as a reminder that because I do experience some privileges I am not fully without power. At the same time, this is a perspective whose usefulness is limited and it puts me in danger of being too meek when confronted with a system that always benefits from my saying ‘it could be so much worse.’ 

I do exercise my voice on the page, in small ways in my journalism work and larger ways in this newsletter and my forthcoming book, but often I am doing so not with fervor and conviction but in spite of being tired. The overall sense of exhaustion that has been my experience of being a writer so often reduces all tasks into an uphill battle of simply getting something done. This makes those moments when I see my sense of self alight between the words that I write feel like exceptions to the rule, like wiggling a vestigial appendage and calling it a workout. 

Being tired does not necessarily rob me of dignity as a person and a writer, or my capacity to have a vision for the future, but being overworked does trick me into thinking that I am as deficient in it as I am in time. Or that the only possible state for both is being in short supply. Can a person really get too tired to dream of a better future, and write it as they dream? If this isn’t something that the “system does” already, it at times really feels like it is trying to.

The situation is, then, a contradictory one. It’s an exercise in existing in a superposition of two ideas that pull the heart in opposite directions - that writing can be empowering and that writers are also routinely overworked and underpaid. As

Olga Koutseridi

wrote about recently, traditional systems of publishing are built on the idea that writers, especially young writers, will sell their work for very little money with the hope of gaining acclaim and opportunities later. ”No promise of success justifies exploitation of people. No promise of opportunities, book deals, teaching gigs, is worth the price of human suffering,” she writes in rebuttal and goes on to call for a collective effort to refuse the old, exploitative system and organize and rebuild it into something new. I found myself nodding my head, agreeing with the call mandate that we “do better, together” yet not losing sight that even an essay about how writing needs to change came to me through writing, on a platform that is quickly filling up with traditionally established writers. Another superposition.

The idea of time poverty dates to 1977 and the work of economist Clair Vickery who criticized the official poverty index as being inaccurate because it only accounts for income and not “time resources.” She was writing about households like those run by single parents where a person may be able to afford necessities like food or rent, but still spend too much time on cooking or cleaning to have time for other essential activities like spending time with their children or personal betterment through arts or education. Today, time poverty is an issue across all sorts of households. 

In 2011, data from Gallup found 70% of employed Americans self-reporting that they “never had enough time.” By 2018, this number increased to 80%. Not surprisingly, social science researchers find that people who are materially affluent can leverage some of their income to become more time affluent as well, like paying for cleaners or private chefs. For lower income people and people who are members of disadvantaged groups, being time poor, on the other hand, becomes yet another obstacle to improving their quality of life. 

Writing about sleep poverty specifically, in a 2022 Aeon article, Jonathan White argues

“The fact that sleep disadvantages tend to cluster with other kinds of disadvantage means that those less inclined to exercise their political rights may also be those most in need of them. Policies they might benefit from – including fair compensation for sleep-harming labour – become less likely if they are absent from the process. The desynchronisation of sleep also reduces the overlapping free time in which people can coordinate politically. From protests to party meetings, active citizenship depends on the availability of free time that is shared, and by those not so exhausted as to seek only privacy.”

Studies support this too. One paper published in Nature Human Behavior in 2019, for instance, found that “insufficient sleep predicts lower voter turnout” and underslept people exhibit a decreased “willingness to vote, sign petitions and donate to charities.” White extrapolates these findings in a dark direction, speculating that if the underslept and tired cannot find the time and energy to vote then they may be more accepting to authoritarians that seemingly offer to take the labor of civic decisions off their hands. He writes:

“A tired population is likely to be more accepting of regime types that make fewer demands on their participation. Tiredness impairs an individual’s ability to take decisions for themselves. It inhibits the cognitive functions required for an outlook that is other-oriented, deliberative and action-centered. Political disengagement is one likely outcome, but so is acceptance of charismatic and technocratic forms of rule that vest decision-making in elites.”

Here, again, empirical science adds fuel to the fire of fear, with psychological research finding that “time poverty leads people to a more narrow and concrete style of thinking, focusing more on the immediate "how" rather than the broader "why."” In the wake of the most recent presidential election in the United States and the barrage of post-mortems which assert that voters simply wanted a candidate who would promise that their lives would become immediately and tangibly better, these findings ring true beyond the confines of peer reviewed research. 

It would be much easier for me to speculate on this if I didn’t also have a troubled relationship with sleep. I have a convenient explanation for my five-hours-a-night habit: it started when I was in graduate school and then got worse while I was teaching high school. I am doing neither of those things now, but I am writing a book. The advance for the book was not sufficient for me to take time off from my job and because I don’t come from wealth and have spent my twenties in graduate school my savings weren’t sufficient for that either. So, I wrote the bulk of the book after work and late into the night. 

This sounds unfortunate but reasonable. It may even sound laudable. Underneath the appearance of drive and grit, however, is the messy truth about harmful external structures intertwining with decision making that feels more personal and internal. In a world built on capitalist logics there is social currency to always being busy, especially when that is conflated with being high achieving or being ambitious. It is also easy to confuse the ability to always work with the ability to be good, the resilience in the face of endless tasks with a superior moral character. 

This confusion was handed to me alongside the false promises of the American dream when I immigrated to the United States as a teenager. Graduate school put a new spin on it, as did every workplace where I landed since. Being a writer has been no exception, in my day job, here on Substack, and in selling my book. 

For instance, my literary agent reached out to me, and ultimately decided to represent me, because he read a longform essay I had written about a somewhat odd mathematical concept that also features prominently in quantum physics. I had wanted to write something like that for a long time, but it felt too niche and unsexy to pitch to most publications. When I finally got a chance to write the piece then, it I was genuinely happy to pour time into it. I loved writing that essay, and it certainly helped my writing career. It was also the least I have ever been paid per word by a publication. Writing it barely made a dent in my finances that month - and you can’t pay rent with pride and verbal reassurances about your talent. Truthfully, the teaching job I had at the time paid for the hours I spent being busy with that essay, and bought me subsequent praise and opportunities, not the publication that commissioned it.

I can afford to pay my share of rent now because my writing is dominated by fairly traditional 9-to-5 work in a newsroom of a privately owned magazine. Working in journalism, and very niche journalism at that, has not made me affluent, but it has made it possible for me to get by, even at a time when the industry as a whole seems to be crumbling. It has also plunged me into a world of quick turnaround and readership metrics, all of which often conspire to make me feel if not time poor then at least very time broke. Graduate school was a similarly exhausting experience, albeit more financially ruinous, so I am able to grit my teeth and clench my jaw and come out on the other side of most workdays as a highly performing member of the team. I know that my work brings in lots of readers and potential subscribers and I have at times been praised for this. But I rarely feel successful.

Like studies imply, I feel stuck in the moment and the only future I can imagine is one where my supposed success crumbles because I finally get too tired to get all the work done. What I should probably be worried about instead is that I will get too tired to dream or organize, but the connection between overwork and success is so ingrained in me that it takes a second to remember how artificial it all is. 

I signed the contract that finalized the sale of my book at the end of last January. Now, a little less than a year later, I am scrambling to take one final pass through the 260 page manuscript that I have since pulled together across myriad late nights, weekends, subway commutes to work, and a dozen or so days I did manage to take off from journalism. When the book sold, I had already written the first chapter and I felt confident in the outlines for the remaining eleven. Getting them all done at the pace of about one a month seemed reasonable, especially given the overlap with the years of writing I had put into this newsletter and my technical expertise from a past life as an academic. I don’t want to say that this was a bad estimate of how quickly I can read, research, write and edit, because I am quite confident that when the due date for the manuscript actually comes in a few days, it will be in good enough shape to be handed off to my editor. What I did underestimate, however, is how tired I would be by the end of the process.

A few weeks ago, my partner was out of town for a softball tournament and the ten or so days that I spent in our apartment alone, mostly shuffling myself and my stacks of notes between the desk in our living room and the desk in our home office, made me realize that this year of writing has felt uncannily like my last year of graduate school. Settings aside the fact that the COVID-19 pandemic hit literally two days after I defended my degree, that whole year had been a fairly grim one, starting with an unexpected stay in the ICU and marked by many solitary months of writing my dissertation and teaching to make ends meet. 

My dissertation clocked in at over 200 pages and I am proud of the tone and style in which I wrote it as much as I am of the research that it summarizes. But I barely remember what it felt like to finish it, or whether I was a happier person once my university's administrators signed off on it. I have very few memories from that time overall, other than that I was lonely and tired, that I baked a lot of bread and logged lots of miles at the local indoor track and hours and hours in the neighborhood hot yoga studio. I recently started going to vinyasa classes again, after months of occasionally dabbling in yin yoga only, and found it somewhat reassuring that the years did not change my coping mechanisms all that much. 

But my book is nothing like my dissertation. It is not one last set of dues I have to pay before I can close a particular chapter of my life, it is not a project that I couldn’t opt out of, and it is not work whose front page will carry names of any “research director” or a different authority figure other than me. For years, I really wanted to write this book. It has been painfully easy to forget that in this final stretch of working on it. It has been painfully easy to forget that I am the future that that past version of me dreamed about when they weren’t too tired to do so.

Romantic notions of what it is like to be a writer really do not hold up to scrutiny in today’s media environment, in today’s publishing industry, and in today’s economy. But when I settle in at my desk to write, I feel calm in how much I am still in love with writing. Committing myself to a vision of myself as a writer, even just a very tired one, is what has afforded me those glimmering moments of envisioning a different life, of being able to imagine it for myself instead of just imagining it abstractly. When those moments pass, I grieve them - and try to remember that grief can be a place where change takes root.

My book is a memoir, which makes it inherently backwards looking, but the act of writing it has been an opportunity for me to practice my future, in the same way that cooking vegan meals for my loved ones is, or wearing clothes that make me look like the person that I feel that I am. This is not practice for a future life where I am a more traditionally established writer or maybe a more affluent one, it’s a practice for being a person who can afford to reflect, who can afford to remember, who can afford to construct their own internal model for what existing in the physical world is all about, and who can afford to linger in the sense of beauty that words can provide and to commune with others who do the same. 

I wish it could have been easier to find time to write my book and I wish I had had the means to write it only when I was rested and brimming with inspiration. I wish I had been braver in the past and stood up for myself more when it came to my labor, or that I had kept the anxious capitalist who has long been trying to colonize my heart and mind more in check when it came to denying myself relaxation and comfort. I know there are no bootstraps I could grab onto to pull myself out of time poverty. But, in yet another contradiction, if being overly busy and overworked has put me at risk of becoming dull, complacent, and stuck in the narrowness of now, then finding time to write this book gave me at least some chance to stand my ground against that.

***

Remember those physical systems that presumably never relax, that never even out and forever maintain some ordered structure instead? Anderson’s work in the 1950s suggested that not only do such systems have to be quantum but they also have to be filled with atoms or other particles that essentially don’t belong. 

He studies charged particles moving through a one-dimensional wire and though each of them should have been able to lose its particle-like shape and edges and instead become one extended, even, calm quantum wave, Anderson found that if the wire was filled with “dirt,” such as interloper atoms of a different material, this process would get thwarted. An electron that was meant to become one low crest, and barely one at that, would be forced into a narrow, peaked shape squeezed between two or more such dirt particles. Its “eigenstate” would become “localized.” There was now extra structure in the wire and it prevented it from following the thermodynamic edict of relaxation.

Can something similar happen in systems where there are many particles and they can all interact, or “talk to each other” and coordinate? In 2016, John Imbrie at the University of Virginia seemed to provide a rigorous mathematical proof that the answer is affirmative. Even a so-called many-body system can assume a quantum state that resists thermalization forever if you disrupt and distract it with enough dirt. But Imbrie’s proof only worked when he made a specific assumption about the energies of those particles, and other physicists have now spent years trying to understand whether the proof can work without it too. 

The study that I reported on in October has a similar problem. It does rigorously prove that a system can beat cosmically mandated relaxation - but that system has to have infinitely many dimensions. Physics is an art of approximations to such an extent that it is not impossible to experimentally create systems that in some sense approximate some sort of infinity. So, remarkably, being infinite-dimensional does not always equate to being fully unphysical. But it certainly makes it harder to argue that the issue has been resolved. Frustratingly, thinking about physical systems, be they idealized mathematical versions on paper or finicky atoms and messy wires in the lab, leads to the same places as any consideration of what it means to relax in real life: it gets complicated, and it requires nuance.

One physicist told me as much, conceding that even if states that can avoid relaxation forever and leverage quantum effects to not give into the second law do exist beyond a few very specific cases, they would be very fragile. Maybe they would not give into thermalization if you left them alone under ideal circumstances, but that doesn’t mean that they would be resilient to all of your interventions, that there would not be a way to shake the system up and let it settle into a more even state, a state where no-one is forced to be narrow and tight and peaked. 

As I often do, I took comfort in this, choosing to treat it as a research-paper-turned-divination, a hint from the cosmos that I am also allowed to relax, that the state of having ordered my life into a schedule of writing and then more writing, and then more writing will not manage to stay rigid forever. There is of course the question of conditions under which such a state forms - I promise to be more angry about them once I am less tired.

Best,

Karmela 

Upcoming on Ultracold: Media/Diet for December and my annual birthday letter!