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Information-driven engines that rectify thermal fluctuations are a modern realization of the Maxwell-demon thought experiment. We introduce a simple design based on a heavy colloidal particle, held by an optical trap and immersed in water. Using a carefully designed feedback loop, our experimental realization of an “information ratchet” takes advantage of favorable “up” fluctuations to lift a weight against gravity, storing potential energy without doing external work. By optimizing the ratchet design for performance via a simple theory, we find that the rate of work storage and velocity of directed motion are limited only by the physical parameters of the engine: the size of the particle, stiffness of the ratchet spring, friction produced by the motion, and temperature of the surrounding medium. Notably, because performance saturates with increasing frequency of observations, the measurement process is not a limiting factor. The extracted power and velocity are at least an order of magnitude higher than in previously reported engines.

In some situations in stochastic thermodynamics not all relevant slow degrees of freedom are accessible. Consequently, one adopts an effective description involving only the visible degrees of freedom. This gives rise to an apparent entropy production that violates standard fluctuation theorems. We present an analytically solvable model illustrating how the fluctuation theorems are modified. Furthermore, we define an alternative to the apparent entropy production: the marginal entropy production which fulfills the fluctuation theorems in the usual form. We show that the non-Markovianity of the visible process is responsible for the deviations in the fluctuation theorems.

Micro-reversibility plays a central role in thermodynamics and statistical mechanics. It is used to prove that systems in contact with a thermal bath relax to canonical ensembles. However, a problem arises when trying to reproduce this proof for classical and quantum collisional baths, i.e. particles at equilibrium interacting with a localized system via collisions. In particular, micro-reversibility appears to be broken and some models do not thermalize when interacting with Maxwellian particles. We clarify these issues by showing that micro-reversibility needs the invariance of evolution equations under time reversal plus the conservation of phase space volume in classical and semiclassical scenarios. Consequently, all canonical variables must be considered to ensure thermalization. This includes the position of the incident particles which maps their Maxwellian distribution to the effusion distribution. Finally, we show an example of seemingly plausible collision rules that do not conserve phase-space volume, and consequently violate the second law.The first issue that we address concerns the very formulation of the micro-reversibility condition. The generic statement of micro-reversibility is that the probability to observe a transition Γ → Γ is equal to the probability of the reverse transitionΓ →Γ. Here, Γ and Γ are arbitrary microscopic states of a physical system andΓ the time-reversal state of Γ. The mathematical expression of this statement reads (we provide a more detailed description later on, in Sec. 2):However, this equality immediately poses a problem if the variable Γ is continuous. In that case, ρ(Γ |Γ) is a density in Γ , whereas ρ(Γ|Γ ) is a density inΓ. Consequently, when the two conditional probabilities are compared, one has to take into account the transformation of the volume elements dΓ and dΓ . In classical systems, Liouville's theorem warrants the conservation of volume, implying dΓ = dΓ , and resolves the problem. But micro-reversibility is also relevant for quantum and semi-classical systems with states parametrized by continuous variables Γ, such as Wigner distributions in phase space or wave packets centered around a given position and velocity [9,10]. In the first case, for instance, it has been shown that there is no equivalent Liouville-like theorem, that is, unitary evolution does not necessarily conserve the phase-space volume [11]. Therefore, it is necessary to explicitly check the micro-reversibility condition, Eq. (1), in those quantum and semi-classical scenarios.The second issue concerns the role of micro-reversibility in the relaxation of a system towards equilibrium. For a classical system in contact with a thermal bath, the micro-reversibility condition applies to micro-states Γ = (x, y) of the global system, consisting of the system itself (x) and the bath (y). The bath variables can be eliminated by multiplying Eq. (1) by the equilibrium distribution ρ eq (y) and integrating over y and y . This procedure, which we describe in detail in Sec. 2.1, is especially relevant...