{"product_id":"reversa-loschmidts-reversal-paradox-physics-t-shirt","title":"Reversa – Loschmidt's Reversal Paradox Physics T-Shirt","description":"\u003cp\u003eReversa flips every molecule's velocity, and the gas should un-mix. So why does time only run one way?\u003c\/p\u003e\u003ch3\u003eThe Physics\u003c\/h3\u003e\u003cp\u003eNewton's laws run equally well backwards, yet Boltzmann's H-theorem says a gas always heads toward equilibrium. Reverse every velocity and the gas would retrace its steps, so the arrow of time cannot come from the dynamics alone. The H-theorem rests on the molecular-chaos assumption.\u003c\/p\u003e\u003cp\u003e\u003cstrong\u003eH = ∫ f ln f d³v,   dH\/dt ≤ 0\u003c\/strong\u003e\u003c\/p\u003e\u003cul\u003e\n\u003cli\u003eH: Boltzmann's H function (dimensionless, per volume)\u003c\/li\u003e\n\u003cli\u003ef: velocity distribution (s³\/m⁶)\u003c\/li\u003e\n\u003cli\u003ed³v: velocity-space volume element (m³\/s³)\u003c\/li\u003e\n\u003cli\u003et: time (s)\u003c\/li\u003e\n\u003c\/ul\u003e\u003cp\u003eJosef Loschmidt raised the objection in 1876.\u003c\/p\u003e\u003cp\u003e\u003cem\u003eHonest caveat:\u003c\/em\u003e This does not break the second law. Why the past had low entropy is still debated.\u003c\/p\u003e\u003ch3\u003eOn the shirt\u003c\/h3\u003e\u003cp\u003eFront: Reversa, the pixel-art character, with the title. Back: the reversibility of Newton's laws, Boltzmann's H-theorem, the molecular-chaos note and the 1876 objection. Printed on a unisex tee.\u003c\/p\u003e","brand":"Printify","offers":[{"title":"S \/ White","offer_id":50936458805351,"sku":"52492985517795476735","price":29.99,"currency_code":"USD","in_stock":true},{"title":"S \/ Black","offer_id":50936458838119,"sku":"27153157856116651434","price":29.99,"currency_code":"USD","in_stock":true},{"title":"M \/ White","offer_id":50936458870887,"sku":"75005572840363112169","price":29.99,"currency_code":"USD","in_stock":true},{"title":"M \/ Black","offer_id":50936458903655,"sku":"16658486355801121853","price":29.99,"currency_code":"USD","in_stock":true},{"title":"L \/ White","offer_id":50936458936423,"sku":"24065271096957195599","price":29.99,"currency_code":"USD","in_stock":true},{"title":"L \/ Black","offer_id":50936458969191,"sku":"54830085803767263488","price":29.99,"currency_code":"USD","in_stock":true},{"title":"XL \/ White","offer_id":50936459001959,"sku":"60938023658904247728","price":29.99,"currency_code":"USD","in_stock":true},{"title":"XL \/ Black","offer_id":50936459034727,"sku":"21508821838431644940","price":29.99,"currency_code":"USD","in_stock":true},{"title":"2XL \/ White","offer_id":50936459067495,"sku":"13918356242411052136","price":29.99,"currency_code":"USD","in_stock":true},{"title":"2XL \/ Black","offer_id":50936459100263,"sku":"58238387348326555283","price":29.99,"currency_code":"USD","in_stock":true},{"title":"3XL \/ White","offer_id":50936459133031,"sku":"11075905286663981970","price":29.99,"currency_code":"USD","in_stock":true},{"title":"3XL \/ Black","offer_id":50936459165799,"sku":"15732902497135046563","price":29.99,"currency_code":"USD","in_stock":true},{"title":"4XL \/ White","offer_id":50936459198567,"sku":"17186272781191398963","price":29.99,"currency_code":"USD","in_stock":true},{"title":"4XL \/ Black","offer_id":50936459231335,"sku":"33777783714081753652","price":29.99,"currency_code":"USD","in_stock":true},{"title":"5XL \/ White","offer_id":50936459264103,"sku":"12040611585280646973","price":29.99,"currency_code":"USD","in_stock":true},{"title":"5XL \/ Black","offer_id":50936459296871,"sku":"76383340816734682099","price":29.99,"currency_code":"USD","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0596\/8746\/9159\/files\/loschmidt-paradox_front_02_white.png?v=1793595249","url":"https:\/\/pixelatedphysics.com\/tr\/products\/reversa-loschmidts-reversal-paradox-physics-t-shirt","provider":"Pixelated Physics","version":"1.0","type":"link"}