{"product_id":"erasa-forgetting-costs-heat-physics-t-shirt","title":"Erasa – Forgetting Costs Heat Physics T-Shirt","description":"\u003cp\u003eErasa wipes a bit clean and a puff of heat drifts off. Forgetting is never free.\u003c\/p\u003e\u003ch3\u003eThe Physics\u003c\/h3\u003e\u003cp\u003eErasing one bit of information, resetting a memory to a standard state no matter what it held, must on average release at least k_B T ln 2 of heat into the surroundings. At 300 K that is 2.87 × 10⁻²¹ J, about 0.018 eV. The cost comes from erasure; it does not apply to every logical step.\u003c\/p\u003e\u003cp\u003e\u003cstrong\u003e⟨Q⟩ ≥ k_B T ln 2\u003c\/strong\u003e\u003c\/p\u003e\u003cul\u003e\n\u003cli\u003eQ: heat released per erased bit (J)\u003c\/li\u003e\n\u003cli\u003ek_B: Boltzmann constant, 1.380649 × 10⁻²³ J\/K\u003c\/li\u003e\n\u003cli\u003eT: temperature (K)\u003c\/li\u003e\n\u003cli\u003eln 2: ≈ 0.693 (dimensionless)\u003c\/li\u003e\n\u003c\/ul\u003e\u003cp\u003eRolf Landauer proposed it in 1961, and Bérut et al. measured it with a single trapped colloidal bead (Nature, 2012).\u003c\/p\u003e\u003cp\u003e\u003cem\u003eHonest caveat:\u003c\/em\u003e It applies to logically irreversible erasure, not to every computation.\u003c\/p\u003e\u003ch3\u003eOn the shirt\u003c\/h3\u003e\u003cp\u003eFront: Erasa, the pixel-art character, with the title. Back: the Landauer bound, its value at 300 K and the 1961 and 2012 sources. Printed on a unisex tee.\u003c\/p\u003e","brand":"Printify","offers":[{"title":"S \/ White","offer_id":50936494948455,"sku":"83172230646913094383","price":29.99,"currency_code":"USD","in_stock":true},{"title":"S \/ Black","offer_id":50936494981223,"sku":"12935968685006098636","price":29.99,"currency_code":"USD","in_stock":true},{"title":"M \/ White","offer_id":50936495013991,"sku":"67054506673148784362","price":29.99,"currency_code":"USD","in_stock":true},{"title":"M \/ Black","offer_id":50936495046759,"sku":"15835748932219440946","price":29.99,"currency_code":"USD","in_stock":true},{"title":"L \/ White","offer_id":50936495079527,"sku":"24803846728901469585","price":29.99,"currency_code":"USD","in_stock":true},{"title":"L \/ Black","offer_id":50936495112295,"sku":"10925534457341228532","price":29.99,"currency_code":"USD","in_stock":true},{"title":"XL \/ White","offer_id":50936495145063,"sku":"30702337848225688868","price":29.99,"currency_code":"USD","in_stock":true},{"title":"XL \/ Black","offer_id":50936495177831,"sku":"16796717017677971861","price":29.99,"currency_code":"USD","in_stock":true},{"title":"2XL \/ White","offer_id":50936495210599,"sku":"29612579883535369727","price":29.99,"currency_code":"USD","in_stock":true},{"title":"2XL \/ Black","offer_id":50936495243367,"sku":"30233231273979512045","price":29.99,"currency_code":"USD","in_stock":true},{"title":"3XL \/ White","offer_id":50936495276135,"sku":"11521486384717058922","price":29.99,"currency_code":"USD","in_stock":true},{"title":"3XL \/ Black","offer_id":50936495308903,"sku":"22491118002802289328","price":29.99,"currency_code":"USD","in_stock":true},{"title":"4XL \/ White","offer_id":50936495341671,"sku":"17456635871522125706","price":29.99,"currency_code":"USD","in_stock":true},{"title":"4XL \/ Black","offer_id":50936495374439,"sku":"26443990823853313283","price":29.99,"currency_code":"USD","in_stock":true},{"title":"5XL \/ White","offer_id":50936495407207,"sku":"13323625298108891061","price":29.99,"currency_code":"USD","in_stock":true},{"title":"5XL \/ Black","offer_id":50936495439975,"sku":"85400734677753941233","price":29.99,"currency_code":"USD","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0596\/8746\/9159\/files\/landauer-limit_front_01_white.png?v=1793595361","url":"https:\/\/pixelatedphysics.com\/it\/products\/erasa-forgetting-costs-heat-physics-t-shirt","provider":"Pixelated Physics","version":"1.0","type":"link"}