In conventional fluids, viscosity depends on temperature according to a strict relationship. To change this relationship, one must change the molecular nature of the fluid. Here, we create a metafluid whose properties are derived not from the properties of molecules but rather from chaotic waves excited on the surface of vertically agitated water. By making direct rheological measurements of the flow properties of our metafluid, we show that it has independently tunable viscosity and temperature, a quality that no conventional fluid possesses. We go on to show that the metafluid obeys the Einstein relation, which relates many-body response (viscosity) to single-particle dynamics (diffusion) and is a fundamental result in equilibrium thermal systems. Thus, our metafluid is wholly consistent with equilibrium thermal physics, despite being markedly nonequilibrium. Taken together, our results demonstrate a type of material that retains equilibrium physics while simultaneously allowing for direct programmatic control over material properties.Faraday waves | metafluid | emergent thermodynamics M aterials science seeks not only to understand but also to control the properties of matter. To do so, one must dynamically change the nature of conventional materials at the molecular scale. Recent work circumvents this problem by rejecting the molecule as the fundamental unit and substituting a macroscopic structural element. This approach has successfully created metamaterials with novel optical (1-3), acoustic (4-6), mechanical (7-9), and fluid properties (10, 11) that would otherwise be impossible. However, this approach comes at a cost: by deriving their properties from macroscopic, nonequilibrium, or anisotropic elements, these materials necessarily abandon the physics of thermal systems. In this work, using a combination of active and passive rheology, we show that macroscopic chaotic surface waves on a vertically agitated fluid form a fully thermal metafluid with dynamically tunable material properties. In contrast to a conventional fluid in which viscosity and temperature are inextricably linked, we show that these quantities are independently tunable in our system. We further demonstrate that by satisfying the barest criteria of isotropy and steady-state chaos [as required by kinetic theory (12, 13)], we have created a system that obeys the Einstein relation (14). Thus, despite being macroscopic and nonequilibrium, the system is well described by equilibrium thermal physics.The "molecules" of our metafluid are chaotic Faraday waves (15, 16), generated in a water-filled aluminum dish that is vertically oscillated with rms amplitude A s and at frequency f s (Fig. 1 A and C; see Materials and Methods for technical details). The waves uniformly cover the surface of the water and experience significant pinning only at the boundary, far from where our measurements are conducted. The chaos and wave density is holistically steady state, although the existence of a particular wave is transient. Thus, "collisions" in our syste...

We have constructed a macroscopic driven system of chaotic Faraday waves whose statistical mechanics, we find, are surprisingly simple, mimicking those of a thermal gas. We use real-time tracking of a single floating probe, energy equipartition, and the Stokes-Einstein relation to define and measure a pseudotemperature and diffusion constant and then self-consistently determine a coefficient of viscous friction for a test particle in this pseudothermal gas. Because of its simplicity, this system can serve as a model for direct experimental investigation of nonequilibrium statistical mechanics, much as the ideal gas epitomizes equilibrium statistical mechanics.

We use a bath of chaotic surface waves in water to mechanically and macroscopically mimic the thermal behavior of a short articulated chain with only nearest-neighbor interactions. The chaotic waves provide isotropic and random agitation to which a temperature can be ascribed, allowing the chain to passively explore its degrees of freedom in analogy to thermal motion. We track the chain in real time and infer end-to-end potentials using Boltzmann statistics. We extrapolate our results, by using Monte Carlo simulations of self-avoiding polymers, to lengths not accessible in our system. In the long chain limit we demonstrate universal scaling of the statistical parameters of all chains in agreement with well-known predictions for self-avoiding walks. However, we find that the behavior of chains below a characteristic length scale is fundamentally different. We find that short chains have much greater compressional stiffness than would be expected. However, chains rapidly soften as length increases to meet with expected scalings.Anyone who has ever put the wrong weight motor oil into a car engine can attest to the fact that the length of a chain molecule largely determines its mechanics [1]. A low-weight oil may be too thin and a high-weight oil too viscous for efficient operation. Biopolymers such as DNA also evidence changing mechanical behavior with changing length. Recent work shows that short strands are far more flexible than would be expected from simply scaling down the behavior of long strands [2]. Understanding this scale dependence in polymers is crucial to creating new materials, as is being done with polymer thin films [3, 4] and so-called "DNA origami" [5,6]. Polymer mechanics is well explored in the coarse-grained sense, with many established methods for direct measurement [7][8][9] and simulation [10][11][12][13]. However, there is scant experimental evidence directly relating whole polymer mechanical properties to behavior at the single bond level. These questions have been addressed in macroscopic granular polymer studies [14,15] however such systems lack a thermodynamic temperature, muddying the link to true thermal systems. Statistical physics predicts [16], and empirical studies confirm [17] that the end-to-end potential of a sufficiently long polymer chain is harmonic, regardless of the microscopic interactions. Similarly, universalities are predicted for the scaling of statistical parameters (i.e., variance and mean) of both bond winding angle [18] and linear dimension [19,20] in a polymer chain when considered as a self-avoiding walk (SAW). While this is a powerful and robust result regarding the chain-scale mechanics, it does little to elucidate the behavior towards the monomer scale, as it does not address short chains.In this paper we build a macroscopic analog to polymer physics in a bottom-up fashion which allows us to observe not only chain-scale but also true monomer-scale behavior. We find that short polymer chains exhibit behavior fundamentally different than that predicted for thei...