Abstract
Characterising causal structure is an activity that is ubiquitous across the sciences. Causal models are representational devices that can be used as oracles for future interventions, to predict how values of some variables will change in response to interventions on others. Recent work has generalised concepts from this field to situations involving quantum systems, resulting in a new notion of quantum causal structure. A key concept in both the classical and quantum context is that of an intervention. Interventions are the controlled operations required to identify causal structure and ultimately the feature that endows causal models with empirical meaning. Although interventions are a crucial feature of both the classical and quantum causal modelling frameworks, to date there has been no discussion of their physical basis. In this paper, we consider interventions from a physical perspective and show that, in both the classical and quantum case, they are constrained by the thermodynamics of measurement and feedback in open systems. We demonstrate that the perfect “atomic” or “surgical” interventions characterised by Pearl’s famous do-calculus are physically impossible, and this is the case for both classical and quantum systems.
Highlights
Causal reasoning is indispensable in science, medicine, economics, and many aspects of every day life
Using the example of coarse-grained position measurements on a thermalised simple harmonic oscillator we show how the uncertainty principle determines the thermodynamic costs of an intervention on a quantum system
We show that an intervention is constrained by the thermodynamics of measurement and feedback in open systems
Summary
Causal reasoning is indispensable in science, medicine, economics, and many aspects of every day life. We approach this question by considering the abstract notion of an intervention from a physical perspective Using examples from both classical and quantum mechanics, we ask whether thermodynamic principles place any constraints on the nature of local interventions. In order to apply this rather abstract definition to mechanical systems, we define interventions in terms of stochastic control theory based on measurement. This makes dynamics irreversible and identifies the source of causal asymmetry as unmodelled noise.
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