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It is not the case that The forward-evolved set U_t'(C) need not screen off A and B if the dynamics are irreversible and information about C is thermodynamically degraded by t'.
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Reasons For
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Reason for
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1.
Screening-off is a causal property independent of information accessibility; irreversibility affects epistemic states, not underlying causal structure.
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2.
Forward evolution U_t'(C) operates on the same dynamical system; if C screened off A,B initially, thermodynamic degradation doesn't create new causal pathways.
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3.
Degraded information about C differs from loss of C itself; statistical dependence between A and B may persist even if C's state becomes unknowable.
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Reasons Against
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Reason against
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1.
Irreversible dynamics destroy correlational structure: information about C's past becomes unrecoverable, so U_t'(C) cannot preserve screening-off relations.
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2.
Thermodynamic degradation of C means entropy increase decouples C from its causal effects, allowing A and B to develop independent predictive power.
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3.
Screening-off requires conditional independence that depends on information structure; information loss fundamentally alters conditional probability relationships.
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