  Collective behaviors displayed by groups of social animals are observed
frequently in nature. Understanding and predicting the behavior of complex
biological systems is dependent on developing effective descriptions and
models. While collective animal systems are characteristically non-equilibrium,
we can employ concepts from equilibrium statistical mechanics to motivate the
measurement of material-like properties in laboratory animal aggregates. Here,
we present results from a new set of experiments that utilize high speed
footage of two-dimensional schooling events, particle tracking, and projected
static and dynamic light fields to observe and control the behavior of
negatively phototaxic fish schools ($\textit{Hemigrammus}$ $\textit{bleheri}$).
First, we use static light fields consisting of dark circular regions to
produce visual stimuli that confine the schools to a range of areas. We find
that the school has a maximum density independent of group size, and that the
swim pressure increases linearly with number density, suggesting that
unperturbed schools exist on an isotherm. Next, we use dynamic light fields
where the radius of the dark region shrinks linearly with time to compress the
schools. We find that the effective temperature parameter depends on the
compression time and our results are thus consistent with the school having a
constant heat flux. These findings provide further evidence for the utility of
effective thermodynamic descriptions descriptions of non-equilibrium systems in
collective animal behavior.
