Geometric structure of thermal cones
- URL: http://arxiv.org/abs/2207.02237v3
- Date: Tue, 13 Dec 2022 16:18:48 GMT
- Title: Geometric structure of thermal cones
- Authors: A. de Oliveira Junior, Jakub Czartowski, Karol \.Zyczkowski, Kamil
Korzekwa
- Abstract summary: We analyse the structure of states that a given state can evolve to (the future thermal cone) or evolve from (the past thermal cone)
For a $d$-dimensional classical state of a system interacting with a heat bath, we find explicit construction of the past thermal cone and the incomparable region.
- Score: 0.0
- License: http://creativecommons.org/licenses/by/4.0/
- Abstract: The second law of thermodynamics imposes a fundamental asymmetry in the flow
of events. The so-called thermodynamic arrow of time introduces an ordering
that divides the system's state space into past, future and incomparable
regions. In this work, we analyse the structure of the resulting thermal cones,
i.e., sets of states that a given state can thermodynamically evolve to (the
future thermal cone) or evolve from (the past thermal cone). Specifically, for
a $d$-dimensional classical state of a system interacting with a heat bath, we
find explicit construction of the past thermal cone and the incomparable
region. Moreover, we provide a detailed analysis of their behaviour based on
thermodynamic monotones given by the volumes of thermal cones. Results obtained
apply also to other majorisation-based resource theories (such as that of
entanglement and coherence), since the partial ordering describing allowed
state transformations is then the opposite of the thermodynamic order in the
infinite temperature limit. Finally, we also generalise the construction of
thermal cones to account for probabilistic transformations.
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