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Welcome to The Nonlinear Library, where we use Text-to-Speech software to convert the best writing from the Rationalist and EA communities into audio. This is: Generalized Stat Mech: The Boltzmann Approach, published by David Lorell on April 12, 2024 on LessWrong. Context There's a common intuition that the tools and frames of statistical mechanics ought to generalize far beyond physics and, of particular interest to us, it feels like they ought to say a lot about agency and intelligence. But, in practice, attempts to apply stat mech tools beyond physics tend to be pretty shallow and unsatisfying. This post was originally drafted to be the first in a sequence on "generalized statistical mechanics": stat mech, but presented in a way intended to generalize beyond the usual physics applications. The rest of the supposed sequence may or may not ever be written. In what follows, we present very roughly the formulation of stat mech given by Clausius, Maxwell and Boltzmann (though we have diverged substantially; we're not aiming for historical accuracy here) in a frame intended to make generalization to other fields relatively easy. We'll cover three main topics: Boltzmann's definition for entropy, and the derivation of the Second Law of Thermodynamics from that definition. Derivation of the thermodynamic efficiency bound for heat engines, as a prototypical example application. How to measure Boltzmann entropy functions experimentally (assuming the Second Law holds), with only access to macroscopic measurements. Entropy To start, let's give a Boltzmann-flavored definition of (physical) entropy. The "Boltzmann Entropy" SBoltzmann is the log number of microstates of a system consistent with a given macrostate. We'll use the notation: SBoltzmann(Y=y)=logN[X|Y=y] Where Y=y is a value of the macrostate, and X is a variable representing possible microstate values (analogous to how a random variable X would specify a distribution over some outcomes, and X=x would give one particular value from that outcome-space.) Note that Boltzmann entropy is a function of the macrostate. Different macrostates - i.e. different pressures, volumes, temperatures, flow fields, center-of-mass positions or momenta, etc - have different Boltzmann entropies. So for an ideal gas, for instance, we might write SBoltzmann(P,V,T), to indicate which variables constitute "the macrostate". Considerations for Generalization What hidden assumptions about the system does Boltzmann's definition introduce, which we need to pay attention to when trying to generalize to other kinds of applications? There's a division between "microstates" and "macrostates", obviously. As yet, we haven't done any derivations which make assumptions about those, but we will soon. The main three assumptions we'll need are: Microstates evolve reversibly over time. Macrostate at each time is a function of the microstate at that time. Macrostates evolve deterministically over time. Mathematically, we have some microstate which varies as a function of time, x(t), and some macrostate which is also a function of time, y(t). The first assumption says that x(t)=ft(x(t1)) for some invertible function ft. The second assumption says that y(t)=gt(x(t)) for some function gt. The third assumption says that y(t)=Ft(y(t1)) for some function Ft. The Second Law: Derivation The Second Law of Thermodynamics says that entropy can never decrease over time, only increase. Let's derive that as a theorem for Boltzmann Entropy. Mathematically, we want to show: logN[X(t+1)|Y(t+1)=y(t+1)]logN[X(t)|Y(t)=y(t)] Visually, the proof works via this diagram: The arrows in the diagram show which states (micro/macro at t/t+1) are mapped to which other states by some function. Each of our three assumptions contributes one set of arrows: By assumption 1, microstate x(t) can be computed as a function of x(t+1) (i.e. no two microstates x(t) both evolve to the same later microstate x(t+1)). By assumption 2, macrostate y(t) can be comput...
Link to original articleWelcome to The Nonlinear Library, where we use Text-to-Speech software to convert the best writing from the Rationalist and EA communities into audio. This is: Generalized Stat Mech: The Boltzmann Approach, published by David Lorell on April 12, 2024 on LessWrong. Context There's a common intuition that the tools and frames of statistical mechanics ought to generalize far beyond physics and, of particular interest to us, it feels like they ought to say a lot about agency and intelligence. But, in practice, attempts to apply stat mech tools beyond physics tend to be pretty shallow and unsatisfying. This post was originally drafted to be the first in a sequence on "generalized statistical mechanics": stat mech, but presented in a way intended to generalize beyond the usual physics applications. The rest of the supposed sequence may or may not ever be written. In what follows, we present very roughly the formulation of stat mech given by Clausius, Maxwell and Boltzmann (though we have diverged substantially; we're not aiming for historical accuracy here) in a frame intended to make generalization to other fields relatively easy. We'll cover three main topics: Boltzmann's definition for entropy, and the derivation of the Second Law of Thermodynamics from that definition. Derivation of the thermodynamic efficiency bound for heat engines, as a prototypical example application. How to measure Boltzmann entropy functions experimentally (assuming the Second Law holds), with only access to macroscopic measurements. Entropy To start, let's give a Boltzmann-flavored definition of (physical) entropy. The "Boltzmann Entropy" SBoltzmann is the log number of microstates of a system consistent with a given macrostate. We'll use the notation: SBoltzmann(Y=y)=logN[X|Y=y] Where Y=y is a value of the macrostate, and X is a variable representing possible microstate values (analogous to how a random variable X would specify a distribution over some outcomes, and X=x would give one particular value from that outcome-space.) Note that Boltzmann entropy is a function of the macrostate. Different macrostates - i.e. different pressures, volumes, temperatures, flow fields, center-of-mass positions or momenta, etc - have different Boltzmann entropies. So for an ideal gas, for instance, we might write SBoltzmann(P,V,T), to indicate which variables constitute "the macrostate". Considerations for Generalization What hidden assumptions about the system does Boltzmann's definition introduce, which we need to pay attention to when trying to generalize to other kinds of applications? There's a division between "microstates" and "macrostates", obviously. As yet, we haven't done any derivations which make assumptions about those, but we will soon. The main three assumptions we'll need are: Microstates evolve reversibly over time. Macrostate at each time is a function of the microstate at that time. Macrostates evolve deterministically over time. Mathematically, we have some microstate which varies as a function of time, x(t), and some macrostate which is also a function of time, y(t). The first assumption says that x(t)=ft(x(t1)) for some invertible function ft. The second assumption says that y(t)=gt(x(t)) for some function gt. The third assumption says that y(t)=Ft(y(t1)) for some function Ft. The Second Law: Derivation The Second Law of Thermodynamics says that entropy can never decrease over time, only increase. Let's derive that as a theorem for Boltzmann Entropy. Mathematically, we want to show: logN[X(t+1)|Y(t+1)=y(t+1)]logN[X(t)|Y(t)=y(t)] Visually, the proof works via this diagram: The arrows in the diagram show which states (micro/macro at t/t+1) are mapped to which other states by some function. Each of our three assumptions contributes one set of arrows: By assumption 1, microstate x(t) can be computed as a function of x(t+1) (i.e. no two microstates x(t) both evolve to the same later microstate x(t+1)). By assumption 2, macrostate y(t) can be comput...
Support ongoing human narrations of LessWrong's curated posts:www.patreon.com/LWCuratedSource:https://www.lesswrong.com/posts/PhTBDHu9PKJFmvb4p/a-shutdown-problem-proposalNarrated for LessWrong by Perrin Walker.Share feedback on this narration.[Curated Post] ✓[125+ Karma Post] ✓
For my continued exploration of German New Medicine, my friend Lorell joins me to share her personal reflections and healing stories. Lorell is a 4/6 Sacral Generator also on the Cross of Eden. Check out her music here and connect with her on IG here Lorell was also a guest on the German New Medicine stories podcast with Freya Kellet. This is another great resource to learn GNM! --- Support this podcast: https://podcasters.spotify.com/pod/show/emoting-podcast/support
Fall is coming and as the weather cools and the sweaters get snuggly, our thoughts turn to a season of thankfulness.But...what if we chose to find thankfulness and gratitude year round?Today Susan and guest Lorell Lyles, discuss that idea of intentional thankfulness and how it can change our everyday life.You can learn more about Lorell at She Said Yes BridalAnd make sure to follow us on all your social media!!
It's the 4th of July so we thought we celebrate this Summer Day with some WCW Beach Blast! We watched Sting vs. Cactus Jack in a Falls Count Anywhere Match from Beach Blast '92! Plus, a fun and silly episode up top! --- 00:00 - Welcome to the Show 5:24 - LoRell's Chicken Shack Donation 11:07 - Beau's Notes 22:45 - Who's Your Favorite Wrestler? 35:00 - Is It SHITHOUSE?! 45:43 - Back from the Break 52:30 - Tights of the Night 55:30 - Outro --- So who's your favorite wrestler? Let us know! Follow Topé Suicida on Instagram, Twitter, and TikTok. And if you want to reach us via email, we're at topesuicidapod@gmail.com! You can follow Beau everywhere @beaurosser. Mike left the internet, but he might be back this year. Don't forget to subscribe, rate, and review the show! And better still, share it with a friend or two, won't you? Welcome to the SHITHOUSE. --- Send in a voice message: https://podcasters.spotify.com/pod/show/tope-suicida/message Support this podcast: https://podcasters.spotify.com/pod/show/tope-suicida/support
On this episode, I discuss how to scale your business with Facebook Ads with Lorell Lane. She's a Facebook Ads expert and 7 figure coach, and she runs 5 businesses with her husband. During this interview she gets candid about the ups and downs of growing her business. FOLLOW LORELL: https://socialsaleslab.com/ Follow on IG: https://www.instagram.com/lorelllane/?hl=en Follow on TikTok: https://www.tiktok.com/@lorelllane MORE WEALTHY WOMAN: Learn more about Wealthy Woman: http://wealthywomandaily.com Follow the show on Instagram: http://instagram.com/wealthywomanpodcast Follow Doni on IG: http://instagram.com/thedonibrown Follow Doni on TikTok: https://www.tiktok.com/@thedonibrown?lang=en --- Send in a voice message: https://podcasters.spotify.com/pod/show/wealthywoman/message
Episode 126:On this episode, Lorell Diaz joins me, she is a mother, entrepreneur and brain tumor survivor. She shares her story of the miracle of healing and how she reinvented herself to now have a successful woman owned catering and events business. She shares the encouragement of not giving up, believing in yourself and more.Partnering with Hi Hello Labs in Downtown Orlando https://www.hihellolabs.comCreations Cuisine Events https://www.instagram.com/creations.cuisine/ Restaurant https://www.facebook.com/creationscuisinebistro https://www.instagram.com/creationscuisinebistro/Support the showSubscribe to Beauty Marks podcast and leave a review. Follow me on Instagram https://www.instagram.com/elizabethsabby/For questions, comments or collaborations please email: beautymarkspodcast@gmail.com Our website to support visit www.beautymarkspodcast.com
In today's episode, Give or Take hosts Grayson, LoRell, and Josh discuss different views on Black History Month, what they think their greatest achievements will be, and how to maintain a relationship with God in today's world.
In this episode, Give or Take hosts Joshua, LoRell and Grayson discuss New Year's resolutions and how they overcome challenges in their lives.
Name: Lorell Lane Business Name: Social Sales Lab Current Title: CEO Location: Orlando, Fl About Lorell: Lorell uses her personal and professional experiences to help others achieve the financial freedom they deserve. As co-founder of the Social Sales Lab, she teaches small business owners, entrepreneurs, influencers, service-providers and other brands and individuals to launch profitable, game-changing Facebook and Instagram ads. DURING THIS EPISODE YOU'LL LEARN: Why businesses should run ads How social media ads benefit businesses Key steps for setting up your ads The importance of a funnel Common mistakes people make when running ads How ads lead to financial freedom Tips for running ads on a budget For complete show notes and resources mentioned for this episode go to: blacktobusiness.com/130 Thank you so much for listening! Please support us by simply rating and reviewing our podcast!
In this episode, my friend Lorell shares her story of her skin cancer literally falling of INTO HER OWN HANDS. Find me @freyakellet Find Lorell @salixlovermother --- Send in a voice message: https://podcasters.spotify.com/pod/show/freya-kellet/message
On this brand new episode, the host RedNick and Lorell discuss three cases of “mythical creatures” in the Prairie state. Did the supposed Thunderbirds really exist? Is it really a big muddy monster in southern Illinois? And what terrorize the town of Enfield, Illinois in the 1970s? So join us as we look into mysterious creatures in the land of Lincoln.
Jocasta is about to star as Rizzo in the West End revival of Grease.Directed by Nikolai Foster and choreographed by Dame Arlene Phillips, Grease is returning to the Dominion Theatre where it previously ran in 1993. Jocasta recently originated the role of Lady Capulet in the West End production of & Juliet (Shaftesbury Theatre), whilst also understudying the roles of Nurse and Anne. In 2016 Jocasta was nominated for West End Frame's Understudy of the Year Award, for covering the roles of Camila, Daniela and Vanessa in the London production of In The Heights (King's Cross Theatre). Her theatre credits also include: Joanne in Rent (Hope Mill Theatre), Anita in West Side Story (Royal Exchange), Yvonne in Sunshine On Leith (West Yorkshire Playhouse) understudy Deena and Lorell in Dreamgirls (West End), Ghost The Musical (International Tour), Dynamite in Hairspray (UK Tour) and Chicago (Curve). Grease begins performances at the Dominion Theatre from 3rd May 2022. Visit www.greasemusical.co.uk for info and tickets.Hosted by Andrew Tomlins. @AndrewTomlins32 Thanks for listening! Email: andrew@westendframe.co.uk Visit westendframe.co.uk for more info about our podcasts.
"Es Un Mismo Escenario" - Adoración Backstage con Lorell Quiles.
Adoración Backstage - Lorell Quiles (segunda parte)
Adoración Backstage - Lorell Quiles
"¿Estancados o Encantados?" Lorell Quiles - Adoración Backstage
"En el Escenario del Fracaso" - Adoración Backstage con Lorell Quiles
Tesoros Incorruptibles - Adoración Backsatge con Lorell Quiles.
Today we dive into the hot topic of mental health in sports with Beth Lorell. We cover everything from all the commercials you see to the 2021 Summer Olympics and much more. You're not going to want to miss this.
¿Quién es el Culpabe Aquí? - Adoración Backstage con Lorell Quiles.
¿Por qué me siento rechazado? - Lorell Quiles - Adoración Backstage.
"Muriendo de hipocresía" - Adoración Backstage con Lorell Quiles.
Beat The Brit is the only American game show with an English guy answering trivia questions with a weird German dance intro!Lorell is a 2011 Women's Division Track Champion but can she Beat The Brit!? Leave a rating and review wherever you listen. It will help the show out in a big way. If that's not your thing, you can find us on social media here:https://instagram.com/thejubalshowhttps://twitter.com/thejubalshowhttps://www.tiktok.com/@thejubalshow
Alex Fresh kicks off the morning pulling the Hermit during the Daily Vibration, Grandpas sending nude pictures in this Jubal Phone Prank, something happened that no one was ready for in this First Date Follow Up, Jubal Fresh adds some spice to this War of the Roses, this women's Dirty little Secret can end someone else's Dirty little Secret, Elon Musk is in trouble with the U.S. government for a ridiculous reason and Lorell is already a champion so will she Beat The Brit!?
"El perdón escandaloso de Jesús" - Adoración Backstage con Lorell Quiles.
"Si en verdad me amas..." - Adoración Backstage con Lorell Quiles.
¿Discernimiento espiritual o 'don de sospecha'?" - Adoración Backstage con Lorell Quiles.
"Caídas Aparatosas" - Adoración Backstage con Lorell Quiles.
“Rich lied to me about something there was no reason to lie about," said Martinez at the time. "I gave him the opportunity to tell me the truth not once, but twice. He didn't die so I shot him in the head. It wasn't personal. It was business." The interview adds that an accomplice shot Rich originally, but he didn't die. Martinez then stepped in to finish off the deed. The two then dumped Porter's body on City Island, according to the interview. On October 31, 2021, Alpo Martinez was shot and killed in Harlem. Porter's family took to the streets to celebrate Martinez's death, according to New York Daily News. “We waited for a long time for this day to come and we are happy," Porter's niece, Lorell, told the publication. “That's why we're out here celebrating drinking champagne. Everybody's reaction right now is celebrating. It's a celebration for Harlem, period.” --- Support this podcast: https://anchor.fm/oss2389/support
"Nacio de Mujer" es el tema de Lorell Quiles en Adoracion Backstage
"Gracias también por esto" - Adoración Backstage con Lorell Quiles.
"Hice las cosas bien, pero me salieron mal" - Adoración Backstage con Lorell Quiles.
"Un encuentro incómodo" - Adoración Backstage con Lorell Quiles.
"CUANDO LA FIESTA SE ACABA" - Adoración Backstage con Lorell Quiles.
"Lo perdí todo por una mala decisión" - Adoración Backstage con Lorell Quiles.
"Quiero perdonar, pero no puedo" - Adoración Backstage con Lorell Quiles.
"Dentro de lo normal" - Lorell Quilles - Adoración Backsatge.
"El Menos Esperado" - Adoración Backstage con Lorell Quiles.
¡Que esto se acabe ya! - Adoración Backstage con Lorell Quiles.
"Quise ayudar y salí trasquila'o" Adoración Backstage con Lorell Quiles.
"En un mundo de cosas que no puedo manejar" - Adoracón Backstage con Lorell Quiles.
"Todavía Me Cuesta" - Adoración Backstage con Lorell Quiles.
"Estatuas de Sal en mi Cuidad" - Adoración Backstage con Lorell Quiles
Adoración Backstage con Lorell Quiles
"Su Gloria en Casa" Adoración Backstage con Lorell Quiles.
On this episode of The Reminder Remedy, host Alena Conley sits down with Lorell of The Social Sales Lab to talk about finding freedom and purpose in your work. The two momprenuers were able to share how having children forced them to reconsider the how and why of how they run their companies. In this authentic conversation the ladies go beyond just the right "copy" on an ad and really talk about the value in having ads that work for you and your lifestyle.Lorell is the Founder of The Social Sales Lab which focuses on helping business owners master Facebook ads, the customer journey while ultimately creating more freedom and revenue in their businesses.Check out her Free Masterclass here to learn more.Have you joined the TRR Flourishing Women self-coaching community yet? What are you waiting on, your Authentic Happiness quiz is waiting on you HERE.
In this episode, we talk with social media marketing expert Lorell Lane on growing her business to over seven figures with Facebook and Instagram marketing. As well as how you can also get started on building your brand too. Former sales executive turned digital marketer. Throughout her career, she has combined personal branding with professional expertise to gain success in the sales world. Now she teaches other sales pros how to do the same to scale their sales. Website: https://lorelllane.com/ Instagram: https://www.instagram.com/lorelllane/ Facebook: https://www.facebook.com/LorellLane/