Experimental realization of a Szilard engine with a single electron

Abstract

The most succinct manifestation of the second law of thermodynamics is the limitation imposed by the Landauer principle on the amount of heat a Maxwell demon (MD) can convert into free energy per single bit of information obtained in a measurement. We propose and realize an electronic MD based on a single-electron box operated as a Szilard engine, where k B T ln 2 of heat is extracted from the reservoir at temperature T per one bit of created information. The information is encoded in the position of an extra electron in the box.T he work of Maxwell introduced what is now known as the "Maxwell demon" (MD) (1). This idea was quantified later on by Szilard (2), initiating interest in the relationship between information and thermodynamics; see, e.g., refs. 3-6. MD extracts heat from a thermal reservoir at temperature T by observing a thermodynamic system to make a spontaneous, thermally induced, transition into a state with larger-than-average free energy (either because of a larger internal energy or a smaller entropy) and using the feedback to collect this extra free energy as work. Szilard demonstrated that by obtaining a single bit of information as a measurement result of the state of the system, one could collect up to k B T ln 2 useful work, where k B is the Boltzmann constant. Such a direct conversion of heat into work would by itself violate the second law of thermodynamics, because both the measurement and the feedback part of MD operation can in principle be done without generating extra entropy. In particular, a classical measurement can be viewed as a process of copying the state of the system into the memory of the detector. The only fundamentally unavoidable thermodynamic costs of conversion of heat into work by an MD is the creation of information about the state of the measured system. According to the Landauer principle (7-9), erasure of this information generates at least the extracted amount of heat, k B T ln 2 per bit, restoring the agreement with the second law.Whereas these general principles of MD operation are well understood in theory [see, e.g., recent discussions (10-12)], only few experimental realizations of an MD exist (13), and thus far none demonstrates a quantitative connection between the MD output and the obtained information. The goal of this work is to realize a system that demonstrates explicitly the extraction of k B T ln 2 of heat from a thermal reservoir by an MD per one bit of created information. The operating cycle we use is close to the thought experiment suggested by Szilard. It realizes the MD operation using feedback-controlled molecule in a box as the working system. Fig. 1A, from left to right, shows the steps of the operation of such a Szilard engine (SE). The molecule is in equilibrium at temperature T, and the box is divided initially into two equal sections. After the measurement establishes which section the molecule is in, the container is allowed to expand into the full volume, lifting a weight tied to the dividing wall. In doing so, it extracts work from t...

Towards quantum thermodynamics in electronic circuits

“…[32]. But experimentally, Maxwell's demon was realized in such a circuit only very recently [33,34]. Here we briefly discuss the principle of the demon, and the results of the experiments performed on an SEB (see Fig.…”

“…Figure 4b presents a typical outcome of a measurement, similar to those obtained in ref. [33]. It is the histogram of heat dissipated into the bath in about 3000 cycles.…”

Feedback Control in Quantum Transport

“…Of these proposals, the current-governor and Maxwell demon are the most hopeful candidates for experimental realisation in the foreseeable future. Indeed, a Maxwell's demon, similar in many respects to the one described here, has recently been realised in the single-electron box [40]. Such schemes are practicable because, although they take place in quantum-confined nanostructures, they do not rely on quantum coherence for their operation.…”

Maxwell's demon based on a single qubit

“…This part of the cycle is equivalent to that in a classical TLS -see Ref. 11 , although the nonvanishing ∆E 0 creates essential differences in the quantum regime. On reaching point X, a measurement of the qubit state is performed.…”

“…On the level of thought experiments this discussion dates back all the way to Maxwell's demon (MD) 7 and then to Landauer's principle 8 . Till now, majority of the studies, both theoretically and in particular experimentally [9][10][11][12] , have been focusing on the classical regime; see, however, [13][14][15][16][17] and references therein for theories on quantum systems. The aim of this Letter is to present a simple and experimentally feasible quantum MD that can operate at the limit of thermodynamic efficiency.…”