Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The Mpemba index and anomalous relaxation   The Mpemba effect is a counter-intuitive relaxation phenomenon, where a
system prepared at a hot temperature cools down faster than an identical system
initiated at a cold temperature when both are quenched to an even colder bath.
Such non-monotonic relaxations were observed in various systems, including
water, magnetic alloys, polymers, and driven granular gases. We analyze the
Mpemba effect in Markovian dynamics and discover that a stronger version of the
effect often exists for a carefully chosen set of initial temperatures. In this
\emph{strong Mpemba effect}, the relaxation time jumps to a smaller value
leading to exponentially faster equilibration dynamics. The number of such
special initial temperatures defines the \emph{Mpemba index}, whose parity is a
topological property of the system. To demonstrate these concepts, we first
analyze the different types of Mpemba relaxations in the mean field
anti-ferromagnet Ising model, which demonstrates a surprisingly rich Mpemba
phase diagram. Moreover, we show that the strong effect survives the
thermodynamic limit and that it is tightly connected with thermal overshoot --
in the relaxation process, the temperature of the relaxing system can decay
non-monotonically as a function of time. Using the parity of the Mpemba index,
we then study the occurrence of the strong Mpemba effect in a large class of
thermal quench processes and show that it happens with non-zero probability
even in the thermodynamic limit. This is done by introducing the
\emph{isotropic} model for which we obtain analytical lower bound estimates for
the probability of the strong Mpemba effects. Consequently, we expect that such
exponentially faster relaxations can be observed experimentally in a wide
variety of systems.

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The categories of this paper are: alg-geom
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The categories of this paper are: quant-ph
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The categories of this paper are: nlin
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The categories of this paper are: solv-int
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The categories of this paper are: math
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The categories of this paper are: q-alg
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The categories of this paper are: adap-org
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The categories of this paper are: nucl-ex
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The categories of this paper are: dg-ga
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The categories of this paper are: hep-ex
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The categories of this paper are: econ
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The categories of this paper are: cmp-lg
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The categories of this paper are: mtrl-th
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The categories of this paper are: q-fin
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The categories of this paper are: nucl-th
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The categories of this paper are: atom-ph