This work sits off on its own: there is almost nobody nearby, but its closest neighbors from the archive study memory and information in non-equilibrium systems. Some look at how memory is trained and how sleep strengthens it, others take apart Maxwell's demon and its quantum variations, and still others fish the laws of nature out of noise. All of them touch in one way or another on the link between information and thermodynamics, but none has stepped beyond the Markovian approximation, in which the environment instantly forgets the past. Our work is the first to show experimentally that the environment's memory, hidden in its internal degrees of freedom, not only exists but can be measured and turned into work.
As a system with memory, the team took a colloidal particle 2.7 micrometers in diameter in a viscoelastic micellar solution. The particle was held by an optical tweezer in a harmonic trap, and its position was recorded at 100 Hz with a precision of 5 nanometers. To reach the hidden degrees of freedom, they used a double-measurement protocol: at time t_i the particle's position was compared with a threshold, and after a delay δt a second identical measurement was made. This yielded four possible states (|00⟩, |01⟩, |10⟩, |11⟩), each correlating differently with the thermal excitations of the micellar network. In parallel, control ensembles were built without accounting for history, to separate the contribution of memory from the effect of initial conditions. Then they measured the relaxation of the particle's potential energy and the Kullback–Leibler information for each state, and also ran work-extraction protocols by shifting the trap at constant speed.
The headline result: the double measurement reveals a backflow of information from the hidden degrees of freedom. For the state |10⟩ at a delay δt of about 1 second, the particle's energy first rises and then decays toward equilibrium, a direct signature of energy transfer from the micellar network to the particle. Quantitatively, this effect is described by an order parameter Φ(δt), which peaks at δt ≈ 1 s. What is more, the work extracted in a double-well potential exceeds the energy stored in the observed coordinate: the normalized work W/¯V_m(0) becomes greater than one. In a single-well trap there is no such excess, because the particle relaxes too quickly to draw energy from the slow modes of the environment. In the double-well case, the barrier slows the particle's relaxation, and the hidden degrees of freedom have time to give up their energy.
This work stands apart from its neighbors in that it is the first to demonstrate experimentally the extraction of work specifically from the environment's memory, rather than from information about the system itself. Neighboring studies either stay in the Markovian regime, discuss non-Markovianity theoretically, or use memory for other purposes (for example, to speed up relaxation). Here, memory acts as a thermodynamic resource in its own right, one that can be measured and converted into work. This pushes the boundaries of information thermodynamics to systems with temporal correlations and provides an experimental tool for studying them.
The topic could develop toward adaptive control protocols that take the state of the hidden degrees of freedom into account and tune the feedback to the current memory of the environment. Double measurements could also serve as an operational criterion for memory erasure: once all information modes have relaxed, the dynamics becomes Markovian, and further measurements yield no gain. In the quantum domain, a similar approach could help characterize and exploit non-Markovian reservoirs for quantum information engines.
The results will influence the design of information engines in complex environments such as biopolymer solutions, active matter, and microfluidic systems, where environmental memory is unavoidable. They will also provide a new tool for experimentally testing the non-equilibrium thermodynamics of open systems with memory.
The next step will be to optimize the work-extraction protocol with the environment's relaxation time in mind and to find the optimal delay between measurements that maximizes the output. It is also worth investigating how the effect scales for different viscoelastic fluids and for systems with several relaxation times.
This work is directly tied to an unsolved problem in the thermodynamics of non-Markovian systems: how to correctly define entropy production and free energy when some degrees of freedom are hidden. Our experiment shows that hidden degrees of freedom are not merely a nuisance but can be a source of useful work, which calls for a revision of the standard boundaries of the second law for systems with memory.
The micellar network in which the particle floated has a relaxation time of about 6 seconds. It is as if the water in a glass remembered the motion of a spoon for several seconds after the spoon was taken out.
The idea of extracting work from hidden memory echoes the plot of Stanisław Lem's short story "The Fourteenth Voyage," in which the protagonist tries to use information about the past to obtain energy, though in the story this leads to paradoxes rather than practical gain.