Abstract
In this work we review the formalism used in describing the thermodynamics of first-order phase transitions from the point of view of maximum entropy inference. We present the concepts of transition temperature, latent heat and entropy difference between phases as emergent from the more fundamental concept of internal energy, after a statistical inference analysis. We explicitly demonstrate this point of view by making inferences on a simple game, resulting in the same formalism as in thermodynamical phase transitions. We show that analogous quantities will inevitably arise in any problem of inferring the result of a yes/no question, given two different states of knowledge and information in the form of expectation values. This exposition may help to clarify the role of these thermodynamical quantities in the context of different first-order phase transitions such as the case of magnetic Hamiltonians (e.g. the Potts model).
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Acknowledgments
SD and JP gratefully acknowledge funding from FONDECYT grant 1140514. JP acknowledges partial support from FONDECYT 11130501. GG acknowledges partial support from FONDECYT 1120603. DG acknowledges funding from CONICYT PhD fellowship 21140914.
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Davis, S., Peralta, J., Navarrete, Y. et al. A Bayesian Interpretation of First-Order Phase Transitions. Found Phys 46, 350–359 (2016). https://doi.org/10.1007/s10701-015-9967-5
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DOI: https://doi.org/10.1007/s10701-015-9967-5