In 1961, Rolf Landauer argued that the erasure of information is a dissipative process. A minimal quantity of heat, proportional to the thermal energy and called the Landauer bound, is necessarily produced when a classical bit of information is deleted. A direct consequence of this logically irreversible transformation is that the entropy of the environment increases by a finite amount. Despite its fundamental importance for information theory and computer science, the erasure principle has not been verified experimentally so far, the main obstacle being the difficulty of doing single-particle experiments in the low-dissipation regime. Here we experimentally show the existence of the Landauer bound in a generic model of a one-bit memory. Using a system of a single colloidal particle trapped in a modulated double-well potential, we establish that the mean dissipated heat saturates at the Landauer bound in the limit of long erasure cycles. This result demonstrates the intimate link between information theory and thermodynamics. It further highlights the ultimate physical limit of irreversible computation.

Shear thickening in dense particulate suspensions was recently proposed to be driven by the activation of friction above an onset stress needed to overcome repulsive forces between particles. Testing this scenario represents a major challenge because classical rheological approaches do not provide access to the frictional properties of suspensions. Here we adopt a different strategy inspired by pressure-imposed configurations in granular flows that specifically gives access to this information. By investigating the quasi-static avalanche angle, compaction, and dilatancy effects in different nonbuoyant suspensions flowing under gravity, we demonstrate that particles in shear-thickening suspensions are frictionless under low confining pressure. Moreover, we show that tuning the range of the repulsive force below the particle roughness suppresses the frictionless state and also the shearthickening behavior of the suspension. These results, which link microscopic contact physics to the suspension macroscopic rheology, provide direct evidence that the recent frictional transition scenario applies in real suspensions.soft matter | shear thickening | dense suspensions | friction D iscontinuous shear thickening occurs in suspensions whose viscosity dramatically increases, sometimes by several orders of magnitude, when the imposed shear rate exceeds a critical value (1). The archetype of such suspensions is cornstarch immersed in water. When sheared vigorously or under impact, these fluids suddenly turn into solids (2). Such remarkable properties play a key role in the flowing behavior of modern concrete (3) and have motivated applications ranging from soft-body protections to sports equipment (4). They also offer promising perspectives for the design of smart fluids with tunable rheology (5). However, the potential realm of development and applications remains largely underexplored due to the lack of understanding of this transition (6).This situation has improved very recently due to new theoretical and numerical works (7,8). Because non-Brownian suspensions of hard frictional particles immersed in a viscous fluid are Newtonian, as imposed by dimensional analysis (8-10), the key idea of these studies is to add a short-range repulsive force between particles in addition to hydrodynamics and contact forces. This repulsive force can, for instance, stem from electrostatic charges or from a specific coating of polymers on the surface of the particle (11). At small shear rate (or small stress), the repulsive force prevents the grains from coming into contact; the suspension thus flows easily as if particles were frictionless. In the remainder of this paper, this state is referred to as frictionless. The viscosity of such a frictionless suspension would diverge at random close packing, whose volume fraction is φrcp = 0.64 for monodisperse spheres. Conversely, at large shear rate (or large stress), the repulsive force is overcome by the hydrodynamic forces and particles are therefore pressed into frictional contacts. The visco...

We measure the energy exchanged between two hydrodynamically coupled micronsized Brownian particles trapped in water by two optical tweezers. The system is driven out of equilibrium by random forcing the position of one of the two particles. The forced particle behaves as it has an "effective temperature" higher than that of the other bead. This driving modifies the equilibrium variances and cross-correlation functions of the bead positions: we measure an energy flow between the particles and an instantaneous cross-correlation, proportional to the effective temperature difference between the two particles. A model of the interaction which is based on classical hydrodynamic coupling tensors is proposed. The theoretical and experimental results are in excellent agreement.

Abstract. -A single bit memory system is made with a brownian particle held by an optical tweezer in a double-well potential and the work necessary to erase the memory is measured. We show that the minimum of this work is close to the Landauer's bound only for very slow erasure procedure. Instead a detailed Jarzynski equality allows us to retrieve the Landauer's bound independently on the speed of this erasure procedure. For the two separated subprocesses, i.e. the transition from state 1 to state 0 and the transition from state 0 to state 0, the Jarzynski equality does not hold but the generalized version links the work done on the system to the probability that it returns to its initial state under the time-reversed procedure.The connection between thermodynamics and information is nowadays a widely studied problem [1][2][3][4][5]. The main questions concern the amount of energy necessary in order to perform a logical operation in a given time and how the information entropy is related to the free energy difference between the initial and final state of this logical operation. In this context the Landauer's principle [6] is very important as it states that for any irreversible logical operation the minimum amount of entropy production is −k B ln(2) per bit commuted by the logical operation, with k B the Boltzmann constant. Specifically a logically irreversible operation is an operation for which the knowledge of the output does not allow to retrieve the initial state, examples are logical AND, OR and erasure. In a recent paper [7] we have experimentally shown that indeed the mini mum amount of work necessary to erase a bit is actually associated with this Landauer's bound which can be asymptotically reached for quasi-static transformations. The question that arises naturally is whether this work corresponds to the free energy difference between the initial and final state of the system. To answer to this question it seems natural to use the Jarzinsky equality [8] which allows one to compute the free energy difference between two states of a system, in contact with a heat bath at temperature T . When such a system is driven from an equilibrium state A to a state B through any continuous procedure, the Jarzynski equality links the stochastic work W st received by the system during the procedure to the free energy difference ∆F = F B − F A between the two states:Where . denotes the ensemble average over all possible trajectories, and β = 1 kBT (see eq. 2 for the precise definition of the work W st ).In this letter we analyze the question of the application of eq. 1 for estimating the ∆F corresponding to the erasure operation in our experiment, in which a colloidal particle confined in a double well potential is used as a single bit memory. We will show that the classical Jarzynski equality (eq. 1) is not useful here but that a detailed Jarzynski Equality [9] allows us to retrieve the Landauer limit independently of the work done on the system during the memory erasure procedure, and to link this work to the proba...