Learning, Information Theory, and Nonequilibrium Statistical Mechanics


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       Learning, Information Theory, & Nonequilibrium




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Memory & Correlation in the Thermodynamics of Maxwellian Demons

11 December 2015

Alexander B. Boyd, UC Davis, and Dibyendu Mandal, UC Berkeley

Abstract: Recent studies on solvable models of Maxwellian demons have introduced various working mechanisms by which information capacity of an environment can be harvested to do useful work. We explore the consequences when the demon has a finite memory and the information-bearing degrees of freedom (IDF) in the environment are correlated. We discover a new functional mechanism for information erasure. We also derive an expression of the second law [1] that is valid under all information processing scenario (with a finite-state demon) and contrast it to a recent proposal [2, 3] which can be violated when both demon-memory and IDF-correlations are important [4, 5]. Our work can be seen as a generalization of the celebrated Landauer principle to arbitrary computation.

SLIDES: Mandal and Boyd.


[1] A. B. Boyd, D. Mandal, and J. P. Crutchfield, “Identifying functional thermodynamics in autonomous Maxwellian ratchets”, arXiv: 1507.01537. LINK: http://arxiv.org/abs/1507.01537

[2] N. Merhav, “Sequence complexity and work extraction,” J. Stat. Mech.: Theor. Exp. (2015) P06037. LINK: http://iopscience.iop.org/article/10.1088/1742-5468/2015/06/P06037/meta

[3] N. Merhav, “Comments on "Identifying Functional Thermodynamics in Autonomous Maxwellian Ratchets" (arXiv:1507.01537v2)”, arXiv: 1508.00203. LINK: http://arxiv.org/abs/1508.00203

[4] D. Mandal, A. B. Boyd, and J. P. Crutchfield, “Memoryless thermodynamics? A reply”, arXiv: 1508.03311. LINK: http://arxiv.org/abs/1508.03311v1

[5] A. B. Boyd, D. Mandal, and J. P. Crutchfield, “The role of memory in autonomous Maxwelliam demons”, in preparation.