Matema¡ticos da Universidade de Nottingham aplicaram a nova teoria qua¢ntica ao paradoxo de Gibbs e demonstraram uma diferença fundamental nos papanãis da informaa§a£o e do controle entre a termodina¢mica qua¢ntica e cla¡ssica.
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)
Ilustração da teoria baseada na mistura de dois gases qua¢nticos. Crédito: Beth Morris, University of Nottingham Maths PhD
Os pesquisadores desenvolveram uma nova versão qua¢ntica de um experimento de pensamento termodina¢mico de 150 anos que pode abrir caminho para o desenvolvimento de motores de calor qua¢nticos.
Matema¡ticos da Universidade de Nottingham aplicaram a nova teoria qua¢ntica ao paradoxo de Gibbs e demonstraram uma diferença fundamental nos papanãis da informação e do controle entre a termodina¢mica qua¢ntica e cla¡ssica. Sua pesquisa foi publicada hoje na Nature Communications .
O paradoxo de Gibbs cla¡ssico levou a descobertas cruciais para o desenvolvimento da termodina¢mica inicial e enfatiza a necessidade de considerar o grau de controle do experimentador sobre um sistema.
A equipe de pesquisa desenvolveu uma teoria baseada na mistura de dois gases qua¢nticos - por exemplo, um vermelho e um azul, de outra forma idaªnticos - que comea§am separados e depois se misturam em uma caixa. No geral, o sistema tornou-se mais uniforme, o que équantificado por um aumento na entropia. Se o observador então colocar a³culos de cor roxa e repetir o processo; os gases parecem iguais, então parece que nada muda. Nesse caso, a mudança de entropia ézero.
Os principais autores do artigo, Benjamin Yadin e Benjamin Morris, explicam: "Nossas descobertas parecem estranhas porque esperamos que quantidades físicas como a entropia tenham significado independente de quem as calcula. Para resolver o paradoxo, devemos perceber que a termodina¢mica diz que coisas aºteis podem ser feitas por um experimentador que tem dispositivos com capacidades especaficas. Por exemplo, um gás de expansão aquecido pode ser usado para acionar um motor. Para extrair trabalho (energia útil) do processo de mistura, vocêprecisa de um dispositivo que pode "ver" a diferença entre os gases vermelhos e azuis. "
Classicamente, um experimentador "ignorante", que vaª os gases como indistinguaveis, não pode extrair trabalho do processo de mistura. A pesquisa mostra que, no caso qua¢ntico, apesar de não conseguir diferenciar os gases, o experimentador ignorante ainda consegue extrair trabalho misturando-os.
Considerando a situação em que o sistema se torna grande, onde o comportamento qua¢ntico normalmente desapareceria, os pesquisadores descobriram que o observador qua¢ntico ignorante pode extrair tanto trabalho como se tivesse sido capaz de distinguir os gases. O controle desses gases com um grande dispositivo qua¢ntico se comportaria de maneira totalmente diferente de uma ma¡quina de calor macrosca³pica cla¡ssica. Esse fena´meno resulta da existaªncia de estados de superposição especiais que codificam mais informações do que as classicamente disponaveis.
O professor Gerardo Adesso disse: “Apesar de um século de pesquisa, hátantos aspectos que não conhecemos ou ainda não entendemos no seio da meca¢nica qua¢ntica. Tal ignora¢ncia fundamental, poranãm, não nos impede de colocar recursos qua¢nticos para um bom uso, como nosso trabalho revela. Esperamos que nosso estudo tea³rico possa inspirar desenvolvimentos interessantes no campo florescente da termodina¢mica qua¢ntica e catalisar novos progressos na corrida contanua por tecnologias aprimoradas qua¢nticas.
"Os motores de calor qua¢nticos são versaµes microsca³picas de nossos aquecedores e refrigeradores dia¡rios, que podem ser realizados com apenas um ou alguns a¡tomos (como já verificado experimentalmente) e cujo desempenho pode ser impulsionado por efeitos qua¢nticos genuanos, como sobreposição e emaranhamento. Atualmente, para ver nosso paradoxo qua¢ntico de Gibbs em um laboratório exigiria controle requintado sobre os parametros do sistema, algo que pode ser possível em sistemas de "rede a³ptica" ajustados ou condensados ​​de Bose-Einstein - estamos atualmente trabalhando para projetar tais propostas em colaboração com grupos experimentais. "