{"product_id":"jarza-the-jarzynski-equality-physics-t-shirt","title":"Jarza – The Jarzynski Equality Physics T-Shirt","description":"\u003cp\u003eJarza pulls a molecular rope again and again. Some pulls cost less than the free energy. Average them the right way and the answer comes out exact.\u003c\/p\u003e\u003ch3\u003eThe Physics\u003c\/h3\u003e\u003cp\u003ePulling a small system out of equilibrium, the work W varies from run to run. The Jarzynski equality says the exponential average of that work gives the equilibrium free-energy difference exactly. Individual pulls can come in below ΔF; on average W ≥ ΔF still holds.\u003c\/p\u003e\u003cp\u003e\u003cstrong\u003e⟨e^(−βW)⟩ = e^(−βΔF),   β = 1\/(k_B T)\u003c\/strong\u003e\u003c\/p\u003e\u003cul\u003e\n\u003cli\u003eW: work done in one run (J)\u003c\/li\u003e\n\u003cli\u003eΔF: free-energy difference (J)\u003c\/li\u003e\n\u003cli\u003eβ: inverse thermal energy (1\/J)\u003c\/li\u003e\n\u003cli\u003ek_B: Boltzmann constant (J\/K)\u003c\/li\u003e\n\u003cli\u003eT: temperature (K)\u003c\/li\u003e\n\u003cli\u003e⟨ ⟩: average over many runs\u003c\/li\u003e\n\u003c\/ul\u003e\u003cp\u003eC. Jarzynski published it in 1997, G. Crooks generalised it in 1999, and Liphardt et al. tested it by pulling single RNA molecules (Science, 2002).\u003c\/p\u003e\u003cp\u003e\u003cem\u003eHonest caveat:\u003c\/em\u003e It is not a second-law violation, and it needs the system to start in equilibrium.\u003c\/p\u003e\u003ch3\u003eOn the shirt\u003c\/h3\u003e\u003cp\u003eFront: Jarza, the pixel-art character, with the title. Back: the equality, the Crooks relation, the below-ΔF note and the 1997, 1999 and 2002 sources. Printed on a unisex tee.\u003c\/p\u003e","brand":"Printify","offers":[{"title":"S \/ White","offer_id":50936637325415,"sku":"31419480944075226282","price":29.99,"currency_code":"USD","in_stock":true},{"title":"S \/ Black","offer_id":50936637358183,"sku":"23976092989679481557","price":29.99,"currency_code":"USD","in_stock":true},{"title":"M \/ White","offer_id":50936637390951,"sku":"26480008794843107415","price":29.99,"currency_code":"USD","in_stock":true},{"title":"M \/ Black","offer_id":50936637423719,"sku":"72991866765740578069","price":29.99,"currency_code":"USD","in_stock":true},{"title":"L \/ White","offer_id":50936637456487,"sku":"17268100353440451916","price":29.99,"currency_code":"USD","in_stock":true},{"title":"L \/ Black","offer_id":50936637489255,"sku":"83820625783897899305","price":29.99,"currency_code":"USD","in_stock":true},{"title":"XL \/ White","offer_id":50936637522023,"sku":"84757700092690190000","price":29.99,"currency_code":"USD","in_stock":true},{"title":"XL \/ Black","offer_id":50936637554791,"sku":"40907701885360682806","price":29.99,"currency_code":"USD","in_stock":true},{"title":"2XL \/ White","offer_id":50936637587559,"sku":"22875986295425978945","price":29.99,"currency_code":"USD","in_stock":true},{"title":"2XL \/ Black","offer_id":50936637620327,"sku":"51425224701974392799","price":29.99,"currency_code":"USD","in_stock":true},{"title":"3XL \/ White","offer_id":50936637653095,"sku":"11012949929552463813","price":29.99,"currency_code":"USD","in_stock":true},{"title":"3XL \/ Black","offer_id":50936637685863,"sku":"35293569606349755748","price":29.99,"currency_code":"USD","in_stock":true},{"title":"4XL \/ White","offer_id":50936637718631,"sku":"40514108109488505602","price":29.99,"currency_code":"USD","in_stock":true},{"title":"4XL \/ Black","offer_id":50936637751399,"sku":"20909769984608330424","price":29.99,"currency_code":"USD","in_stock":true},{"title":"5XL \/ White","offer_id":50936637784167,"sku":"25878868910972607398","price":29.99,"currency_code":"USD","in_stock":true},{"title":"5XL \/ Black","offer_id":50936637816935,"sku":"11545432166848080713","price":29.99,"currency_code":"USD","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0596\/8746\/9159\/files\/jarzynski_front_16_white.png?v=1793595735","url":"https:\/\/pixelatedphysics.com\/sv\/products\/jarza-the-jarzynski-equality-physics-t-shirt","provider":"Pixelated Physics","version":"1.0","type":"link"}