Extracting work from a single heat bath through feedback

Abstract

Work can be extracted from a single heat bath if additional information is available. For the paradigmatic case of a Brownian particle in a harmonic potential, whose position has been measured with finite precision, we determine the optimal protocol for manipulating the center and stiffness of the potential in order to maximize this work in a finite-time process. The bound on this work imposed by a generalized second law inequality involving information can be reached only if both position and stiffness of the potential are controlled and the process is quasistatic. Estimates on the power delivered by such an "information machine" operating cyclically follow from our analytical results.Introduction. -The idea of extracting work from a single heat bath has been investigated for a long time as a putative challenge to the validity of the second law of thermodynamics. Thought experiments such as Maxwell's demon or Szilard's engine, which supposedly violate the second law, were resolved by taking into account the thermodynamic processing of the acquired information through Landauer's principle, which quantifies the cost of information erasure [1,2]. Whether it is the acquisition or the deletion of this information that compensates for the gained work still generates debate [3,4]. The fact, however, that measurements can help to extract work from a single thermal bath has been widely investigated, mainly in theory for the classical [5-8] as well as for the quantum regime [9][10][11][12][13][14], and validated by a recent experiment [15]. This idea is based on the strong link between statistical physics and information theory [16][17][18][19], in particular how the information-theoretic concepts of relative entropy or mutual information can be related to the thermodynamic notion of work [20][21][22]. The generalization of the Jarzynski relation [23] formulated in [24] and the subsequent refinements of the fluctuation theorems [25, 26] take information explicitly into account as a way to extract more work than the corresponding free energy difference from a non-equilibrium process.

Second law and Landauer principle far from equilibrium

“…In fact, the processing of the information I by a physical device will at least offset the gain of work or decrease of total entropy that was realized in the measurement. Without entering in further details, we cite two recent works in which this informationto-work conversion is illustrated, namely one dealing with the case of a Brownian particle in a manipulated potential [39] and the other with a Hamiltonian particle [40]. Note also that a related result was derived in a different context (quantum system subject to feedback control) in [41,42], and verified for the rectification of a Brownian particle moving in a staircase potential [15] (see also [43]).…”

Thermodynamic cost of measurements

“…The mutual information I is positive and it is zero if and only if x and y are independent. If x is the microscopic (or mesoscopic) state of a thermodynamical system in equilibrium with a heat bath at temperature T , then the information obtained can be used to extract heat from the heat bath and convert it into work [1,2,3,7,8,9]. More precisely, let x be the microscopic state (or micro-state) of a thermodynamic system S in contact with a heat bath at temperature T and let p(x) be its equilibrium (canonical) distribution.…”

“…This is not the case in general. Consider for instance the (imperfect) measurement of the position of a Brownian particle as presented in [3]: once one has measured the position of the particle, one should immediately perform a process depending on the measured position in order to convert all of the information into heat. In fact, the particle does not stop moving after the measurement.…”

“…Recently, experimental and theoretical work have specified the relation between information and dissipated work in the thermodynamics of small systems [2,3,4,5,6,7,8,9]. In its traditional formulation, the second law of thermodynamics states that the average work W needed to change the state of a system in contact with a heat bath is bounded from below by the difference in free energy of the final and the initial states:…”

Optimizing Non-ergodic Feedback Engines

“…Subsequent examples by Szilard [1] and others (for example Refs. [2][3][4][5][6]) have revealed that with feedback one can design engines that perform work by extracting energy from a single thermal bath.…”