Artyom Petrosyan

Experimental verification of Landauer/'s principle linking information and thermodynamics

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.

An experimental test of the Jarzynski equality in a mechanical experiment

We have experimentally checked the Jarzynski equality and the Crooks relation (see Jarzynski C., Phys. Rev. Lett., 78 (1997) 2690; Crooks G. E., Phys. Rev. E, 60 (1999) 2721; Jarzynski C., J. Stat. Phys., 98 (2000) 77) on the thermal fluctuations of a macroscopic mechanical oscillator in contact with a heat reservoir. We found that, independently of the time scale and amplitude of the driving force, both relations are satisfied. These results give credit, at least in the case of Gaussian fluctuations, to the use of these relations in biological and chemical systems to estimate the free energy difference ΔF between two equilibrium states (see Ritort F., Seminaire Poincare, 2 (2003) 63; Liphardt J., Dumont S., Smith S. B., Ticono I. jr and Bustamante C., Science, 296 (2002) 1832). An alternative method to estimate ΔF in an isothermal process is proposed too.

Entropy production and time asymmetry in nonequilibrium fluctuations.

The time-reversal symmetry of nonequilibrium fluctuations is experimentally investigated in two out-of-equilibrium systems: namely, a Brownian particle in a trap moving at constant speed and an electric circuit with an imposed mean current. The dynamical randomness of their nonequilibrium fluctuations is characterized in terms of the standard and time-reversed entropies per unit time of dynamical systems theory. We present experimental results showing that their difference equals the thermodynamic entropy production in units of Boltzmanns constant.

Experimental verification of a modified fluctuation-dissipation relation for a micron-sized particle in a nonequilibrium steady state.

A modified fluctuation-dissipation theorem for a nonequilibrium steady state is experimentally checked by studying the position fluctuations of a colloidal particle whose motion is confined in a toroidal optical trap. The nonequilibrium steady state is generated by means of a rotating laser beam which exerts on the particle a sinusoidal conservative force plus a constant nonconservative one. The modified fluctuation-dissipation theorem is perfectly verified by the experimental data. It can be interpreted as an equilibriumlike fluctuation-dissipation relation in the Lagrangian frame of the mean local velocity of the particle.

Steady-state fluctuation relations for systems driven by an external random force

We experimentally study the fluctuations of the work done by an external Gaussian random force on two different stochastic systems coupled to a thermal bath: a colloidal particle in an optical trap and an atomic-force microscopy cantilever. We determine the corresponding probability density functions for different random forcing amplitudes ranging from a small fraction to several times the amplitude of the thermal noise. In both systems for sufficiently weak forcing amplitudes the work fluctuations satisfy the usual steady-state fluctuation theorem. As the forcing amplitude drives the system far from equilibrium, deviations of the fluctuation theorem increase monotonically. The deviations can be recasted to a single master curve which only depends on the kind of stochastic external force.

Thermodynamic time asymmetry in non-equilibrium fluctuations

We here present the complete analysis of experiments on driven Brownian motion and electric noise in an RC circuit, showing that thermodynamic entropy production can be related to the breaking of time-reversal symmetry in the statistical description of these non-equilibrium systems. The symmetry breaking can be expressed in terms of dynamical entropies per unit time, one for the forward process and the other for the time-reversed process. These entropies per unit time characterize dynamical randomness, i.e., temporal disorder, in time series of the non-equilibrium fluctuations. Their difference gives the well-known thermodynamic entropy production, which thus finds its origin in the time asymmetry of dynamical randomness, alias temporal disorder, in systems driven out of equilibrium.

Detailed Jarzynski equality applied to a logically irreversible procedure

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 Landauers bound only for a very slow erasure procedure. Instead a detailed Jarzynski equality allows us to retrieve Landauers bound independently of 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.

Work and dissipation fluctuations near the stochastic resonance of a colloidal particle

We study experimentally the fluctuations of the injected and dissipated energy in a system of a colloidal particle trapped in a double well potential periodically modulated by an external perturbation. The work done by the external force and the dissipated energy are measured close to the stochastic resonance where the injected power is maximum. We show that the steady state fluctuation theorem holds in this system.The orientation fluctuations of the director of a liquid crystal are measured, by a sensitive polarization interferometer, close to the Fréedericksz transition, which is a second-order transition driven by an electric field. We show that, near the critical value of the field, the spatially averaged order parameter has a generalized Gumbel distribution instead of a Gaussian one. The latter is recovered away from the critical point. The relevance of slow modes is pointed out. The parameter of the generalized Gumbel distribution is related to the effective number of degrees of freedom.

Experimental study of out-of-equilibrium fluctuations in a colloidal suspension of Laponite using optical traps

This work is devoted to the study of displacement fluctuations of micron-sized particles in an aging colloidal glass. We address the issue of the validity of the fluctuation dissipation theorem (FDT) and the time evolution of viscoelastic properties during aging of aqueous suspensions of a clay (Laponite RG) in a colloidal glass phase. Given the conflicting results reported in the literature for different experimental techniques, our goal is to check and reconcile them using \emph{simultaneously} passive and active microrheology techniques. For this purpose we measure the thermal fluctuations of micro-sized brownian particles immersed in the colloidal glass and trapped by optical tweezers. We find that both microrheology techniques lead to compatible results even at low frequencies and no violation of FDT is observed. Several interesting features concerning the statistical properties and the long time correlations of the particles are observed during the transition.

Engineered swift equilibration of a Brownian particle

A fundamental and intrinsic property of any device or natural system is its relaxation time relax, which is the time it takes to return to equilibrium after the sudden change of a control parameter [1]. Reducing τrelax, is frequently necessary, and is often obtained by a complex feedback process. To overcome the limitations of such an approach, alternative methods based on driving have been recently demonstrated [2, 3], for isolated quantum and classical systems [4–9]. Their extension to open systems in contact with a thermostat is a stumbling block for applications. Here, we design a protocol, named Engineered Swift Equilibration (ESE), that shortcuts time-consuming relaxations, and we apply it to a Brownian particle trapped in an optical potential whose properties can be controlled in time. We implement the process experimentally, showing that it allows the system to reach equilibrium times faster than the natural equilibration rate. We also estimate the increase of the dissipated energy needed to get such a time reduction. The method paves the way for applications in micro and nano devices, where the reduction of operation time represents as substantial a challenge as miniaturization [10].