Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Thermodynamic uncertainty relations   Bohr and Heisenberg suggested that the thermodynamical quantities of
temperature and energy are complementary in the same way as position and
momentum in quantum mechanics. Roughly speaking, their idea was that a definite
temperature can be attributed to a system only if it is submerged in a heat
bath, in which case energy fluctuations are unavoidable. On the other hand, a
definite energy can only be assigned to systems in thermal isolation, thus
excluding the simultaneous determination of its temperature.
  Rosenfeld extended this analogy with quantum mechanics and obtained a
quantitative uncertainty relation in the form (Delta U) (Delta (1/T)) >= k
where k is Boltzmann's constant. The two `extreme' cases of this relation would
then characterize this complementarity between isolation (U definite) and
contact with a heat bath (T definite). Other formulations of the
thermodynamical uncertainty relations were proposed by Mandelbrot (1956, 1989),
Lindhard (1986) and Lavenda (1987, 1991). This work, however, has not led to a
consensus in the literature.
  It is shown here that the uncertainty relation for temperature and energy in
the version of Mandelbrot is indeed exactly analogous to modern formulations of
the quantum mechanical uncertainty relations. However, his relation holds only
for the canonical distribution, describing a system in contact with a heat
bath. There is, therefore, no complementarity between this situation and a
thermally isolated system.

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The categories of this paper are: math-ph
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The categories of this paper are: funct-an
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The categories of this paper are: patt-sol
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The categories of this paper are: ao-sci
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The categories of this paper are: quant-ph
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The categories of this paper are: astro-ph
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The categories of this paper are: q-bio
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The categories of this paper are: hep-ex
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The categories of this paper are: stat
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The categories of this paper are: nlin
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The categories of this paper are: plasm-ph
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The categories of this paper are: math
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The categories of this paper are: nucl-ex
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The categories of this paper are: bayes-an
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The categories of this paper are: adap-org
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The categories of this paper are: acc-phys