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Before the introduction of Fermi–Dirac statistics in 1926, understanding some aspects of electron behavior was difficult due to seemingly contradictory phenomena. For example, the electronic heat capacity of a metal at room temperature seemed to come from 100 times fewer electrons than were in the electric current.[3] It was also difficult to understand why those emission currents generated by applying high electric fields to metals at room temperature were almost independent of temperature.

The difficulty encountered by the Drude model, the electronic theory of metals at that time, was due to considering that electrons were (according to classical statistics theory) all equivalent. In other words, it was believed that each electron contributed to the specific heat an amount on the order of the Boltzmann constant kB. This statistical problem remained unsolved until the discovery of F–D statistics.

F–D statistics was first published in 1926 by Enrico Fermi[1] and Paul Dirac.[2] According to Max Born, Pascual Jordan developed in 1925 the same statistics which he called Pauli statistics, but it was not published in a timely manner.[4][5][6] According to Dirac, it was first studied by Fermi, and Dirac called it Fermi statistics and the corresponding particles fermions.[7]

F–D statistics was applied in 1926 by Ralph Fowler to describe the collapse of a star to a white dwarf.[8] In 1927 Arnold Sommerfeld applied it to electrons in metals and developed the free electron model,[9] and in 1928 Ralph Howard Fowler and Lothar Wolfgang Nordheim applied it to field electron emission from metals.[10] Fermi–Dirac statistics continues to be an important part of physics.

Distribution of particles over energy[edit]
 
Before the introduction of Fermi–Dirac statistics in 1926, understanding some aspects of electron behavior was difficult due to seemingly contradictory phenomena. For example, the electronic heat capacity of a metal at room temperature seemed to come from 100 times fewer electrons than were in the electric current.[3] It was also difficult to understand why those emission currents generated by applying high electric fields to metals at room temperature were almost independent of temperature.

The difficulty encountered by the Drude model, the electronic theory of metals at that time, was due to considering that electrons were (according to classical statistics theory) all equivalent. In other words, it was believed that each electron contributed to the specific heat an amount on the order of the Boltzmann constant kB. This statistical problem remained unsolved until the discovery of F–D statistics.

F–D statistics was first published in 1926 by Enrico Fermi[1] and Paul Dirac.[2] According to Max Born, Pascual Jordan developed in 1925 the same statistics which he called Pauli statistics, but it was not published in a timely manner.[4][5][6] According to Dirac, it was first studied by Fermi, and Dirac called it Fermi statistics and the corresponding particles fermions.[7]

F–D statistics was applied in 1926 by Ralph Fowler to describe the collapse of a star to a white dwarf.[8] In 1927 Arnold Sommerfeld applied it to electrons in metals and developed the free electron model,[9] and in 1928 Ralph Howard Fowler and Lothar Wolfgang Nordheim applied it to field electron emission from metals.[10] Fermi–Dirac statistics continues to be an important part of physics.

Distribution of particles over energy[edit]
didn't quote
 
I can drive
@LastGerman
didn't quote
In reality, The Fermi–Dirac distribution, which applies only to a quantum system of non-interacting fermions, is easily derived from the grand canonical ensemble.[21] In this ensemble, the system is able to exchange energy and exchange particles with a reservoir (temperature T and chemical potential μ fixed by the reservoir).

Due to the non-interacting quality, each available single-particle level (with energy level ϵ) forms a separate thermodynamic system in contact with the reservoir. In other words, each single-particle level is a separate, tiny grand canonical ensemble. By the Pauli exclusion principle, there are only two possible microstates for the single-particle level: no particle (energy E = 0), or one particle (energy E = ε). The resulting partition function for that single-particle level therefore has just two terms:
1586334013286

and the average particle number for that single-particle level substate is given by
1586334024519

This result applies for each single-particle level, and thus gives the Fermi–Dirac distribution for the entire state of the system.[21]

The variance in particle number (due to thermal fluctuations) may also be derived (the particle number has a simple Bernoulli distribution):

1586334036950

This quantity is important in transport phenomena such as the Mott relations for electrical conductivity and thermoelectric coefficient for an electron gas,[22] where the ability of an energy level to contribute to transport phenomena is proportional to {\displaystyle {\big \langle }(\Delta N)^{2}{\big \rangle }}
{\displaystyle {\big \langle }(\Delta N)^{2}{\big \rangle }}
.
 
Hi, i hope you ascend
 
Feminist theories first emerged as early as 1794 in publications such as A Vindication of the Rights of Woman by Mary Wollstonecraft, "The Changing Woman",[10] "Ain't I a Woman",[11] "Speech after Arrest for Illegal Voting",[12] and so on. "The Changing Woman" is a Navajo Myth that gave credit to a woman who, in the end, populated the world.[13] In 1851, Sojourner Truth addressed women's rights issues through her publication, "Ain't I a Woman". Sojourner Truth addressed the issue of women having limited rights due to men's flawed perception of women. Truth argued that if a woman of color can perform tasks that were supposedly limited to men, then any woman of any color could perform those same tasks. After her arrest for illegally voting, Susan B. Anthony gave a speech within court in which she addressed the issues of language within the constitution documented in her publication, "Speech after Arrest for Illegal voting" in 1872. Anthony questioned the authoritative principles of the constitution and its male-gendered language. She raised the question of why women are accountable to be punished under law but they cannot use the law for their own protection (women could not vote, own property, nor themselves in marriage). She also critiqued the constitution for its male-gendered language and questioned why women should have to abide by laws that do not specify women.

Nancy Cott makes a distinction between modern feminism and its antecedents, particularly the struggle for suffrage. In the United States she places the turning point in the decades before and after women obtained the vote in 1920 (1910–1930). She argues that the prior woman movement was primarily about woman as a universal entity, whereas over this 20-year period it transformed itself into one primarily concerned with social differentiation, attentive to individuality and diversity. New issues dealt more with woman's condition as a social construct, gender identity, and relationships within and between genders. Politically this represented a shift from an ideological alignment comfortable with the right, to one more radically associated with the left.[14]

Susan Kingsley Kent says that Freudian patriarchy was responsible for the diminished profile of feminism in the inter-war years,[15] others such as Juliet Mitchell consider this to be overly simplistic since Freudian theory is not wholly incompatible with feminism.[16] Some feminist scholarship shifted away from the need to establish the origins of family, and towards analyzing the process of patriarchy.[17] In the immediate postwar period, Simone de Beauvoir stood in opposition to an image of "the woman in the home". De Beauvoir provided an existentialist dimension to feminism with the publication of Le Deuxième Sexe (The Second Sex) in 1949.[18] As the title implies, the starting point is the implicit inferiority of women, and the first question de Beauvoir asks is "what is a woman"? [19] A woman she realizes is always perceived of as the "other", "she is defined and differentiated with reference to man and not he with reference to her". In this book and her essay, "Woman: Myth & Reality", de Beauvoir anticipates Betty Friedan in seeking to demythologize the male concept of woman. "A myth invented by men to confine women to their oppressed state. For women, it is not a question of asserting themselves as women, but of becoming full-scale human beings." "One is not born, but rather becomes, a woman", or as Toril Moi puts it "a woman defines herself through the way she lives her embodied situation in the world, or in other words, through the way in which she makes something of what the world makes of her". Therefore, the woman must regain subject, to escape her defined role as "other", as a Cartesian point of departure.[20] In her examination of myth, she appears as one who does not accept any special privileges for women. Ironically, feminist philosophers have had to extract de Beauvoir herself from out of the shadow of Jean-Paul Sartre to fully appreciate her.[21] While more philosopher and novelist than activist, she did sign one of the Mouvement de Libération des Femmes manifestos.

The resurgence of feminist activism in the late 1960s was accompanied by an emerging literature of concerns for the earth and spirituality, and environmentalism. This, in turn, created an atmosphere conducive to reigniting the study of and debate on matricentricity, as a rejection of determinism, such as Adrienne Rich[22] and Marilyn French[23] while for socialist feminists like Evelyn Reed,[24] patriarchy held the properties of capitalism. Feminist psychologists, such as Jean Baker Miller, sought to bring a feminist analysis to previous psychological theories, proving that "there was nothing wrong with women, but rather with the way modern culture viewed them".[25]

Elaine Showalter describes the development of feminist theory as having a number of phases. The first she calls "feminist critique" – where the feminist reader examines the ideologies behind literary phenomena. The second Showalter calls "Gynocritics" – where the "woman is producer of textual meaning" including "the psychodynamics of female creativity; linguistics and the problem of a female language; the trajectory of the individual or collective female literary career and literary history". The last phase she calls "gender theory" – where the "ideological inscription and the literary effects of the sex/gender system" are explored".[26] This model has been criticized by Toril Moi who sees it as an essentialist and deterministic model for female subjectivity. She also criticized it for not taking account of the situation for women outside the west.[27] From the 1970s onwards, psychoanalytical ideas that have been arising in the field of French feminism have gained a decisive influence on feminist theory. Feminist psychoanalysis deconstructed the phallic hypotheses regarding the Unconscious. Julia Kristeva, Bracha Ettinger and Luce Irigaray developed specific notions concerning unconscious sexual difference, the feminine, and motherhood, with wide implications for film and literature analysis.[28]
 
Interesting thread
 

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