  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.
