Summary
The deduction of the first law of thermodynamics from microphysics involves five main problems of long standing:a) the presence of long-range interactions,b) the nontensor character of the gravitational stress-energy density in the curved space-time,c) the integration of the components of tensors or of a complex (like the gravitational stress-energy density) in a curved space,d) the relativistic formulation of thermodynamics,e) the self-energy of particles. We only face problemsa), b) andc) by a field-theoretical approach to gravitation starting from the ideal, «unrenormalized», flat space-time where the stress-energy density turns out to be a tensor. The energy balance is expressed in terms of electromagnetic (e.m.) and gravitational fields, of stresses due to short-range fields (nuclear fields and Poincaré stresses) and of bare-mass densities, which avoid radiation reaction problems and the double computation of the energies associated with the long-range fields (which contribute to real-mass densities). Finally, we express the above quantities in the usual terms of rest-plus-kinetic energies ofparticles andmacroscopic-field energies. However, in this usual form, the first principle of thermodynamics is valid when i) the energies due to the velocity fields of the long-range interactions of the particles of the system considered practically vanish outside the closed boundary surface, and when ii) such «microscopic» energies are much larger than the «macroscopic» energies in the practical region of influence of any particle.
Riassunto
La deduzione della prima legge della termodinamica dalla microfisica coinvolge cinque problemi principali:a) la presenza di interazioni a lungo raggio di azione,b) il carattere non tensoriale della densità di sforzi-energia gravitazionali nello spazio-tempo curvo,c) l’integrazione delle componenti di tensori o di un complesso (come la densità di sforzi ed energia gravitazionali) in uno spazio curvo,d) la formulazione relativistica della termodinamica,e) l’autoenergia delle particelle. Si affrontano solo i problemia), b) ec) con un approccio di teoria di campo alla gravitazione, partendo da uno spazio-tempo ideale e non rinormalizzato, dove la densità di sforzi ed energia risulta essere un tensore. Il bilancio energetico è espresso in termini di campi elettromagnetici (e.m.) e gravitazionali, di sforzi dovuti a campi a corto raggio di azione (campi nucleari e forze di Poincaré) e di densità di masse nude, che evitano problemi di reazione di radiazione e la doppia valutazione delle energie associate ai campi a lungo raggio di azione (che contribuiscono alla densità di massa reale). Infine, si esprimono le grandezze di cui sopra nei termini usuali di energie di riposo e cinetiche delleparticelle e di energie dei campimacroscopici. Tuttavia, in questa forma usuale, il primo principio della termodinamica è valido quando i) le energie dovute ai campi di velocità delle interazioni a lungo raggio di azione delle particelle del sistema considerato praticamente svaniscono all’esterno della superficie chiusa delimitante il sistema e quando ii) tali energie «microscopiche» sono molto più grandi delle energie «macroscopiche» nella regione dove praticamente influisce ciascuna particella.
Резюме
Вывод первого начала термодинамики из микрофизики включает пять основных проблем: 1) наличие длиннодействующих взаимодействий; 2) нетензорный характер гравитационной плотности натяжений-энергии в искривленном пространстве-времени; 3) интегрирование компонент тензоров или комплекса (подобного гравитационной плотности натяжений-энергии) в искривленном пространстве; 4) релятивистская формулировка термодинамики; 5) собственная энергия частиц. Мы рассматриваем только проблемы 1), 2), и 3), используя подход теории поля к гравитации и исходя из идеального, «неперенормируемого» плоского пространства-времени, где плотность натяжений-энергии оказывается тензором. Баланс энергии выражается через электромагнитное и гравитационное поля, натяжения, обусловленные короткодействующими полями (ядерные поля и натяжения Пуанкаре), и плотности затравочных масс, при этом не возникают проблемы реакции излучения и двойное вычисление энергий, связанных с длиннодействующими полями (которые дают вклад в плотности реальных масс). Затем мы выражаем вышеуказанные величины через обычные энергии покоя плюс кинетическую дляцасмиц и энергиимакроскопицеских полей. Однако, в обычной форме первое начало термодинамики справедливо, когда: 1) энергии, обусловленные полями длиннодействующих взаимодействий частиц рассмотренной системы, практически исчезают вне замкнутой граничной поверхности, и 2) такие «микроскопические» энергии много больше, чем «макроскопические» энергии в практической области действия любой частицы.
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Cavalleri, G., Spinelli, G. Hint for a deduction of the first principle of thermodynamics from microphysics. Nuov Cim B 41, 13–28 (1977). https://doi.org/10.1007/BF02726542
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DOI: https://doi.org/10.1007/BF02726542