arXiv subjects
Publications and source records attributed to Michele Campisi.
By modelling heat engines as driven multi-partite system we show that their dissipation can be expressed in terms of the lag (relative entropy) between the perturbed state of each partition and their equilibrium state, and the correlations that build up among the partitions. We illustrate the rich interplay between correlations and lags with a two-qubit device driven by a quantum gate.
A question that is currently highly debated is whether the microcanonical entropy should be expressed as the logarithm of the phase volume (volume entropy, also known as the Gibbs entropy) or as the logarithm of the density of states (surface entropy, also known as the Boltzmann entropy). Rather than postulating them and investigating the consequence of each definition, as is customary, here we adopt a bottom-up approach and construct the entropy expression within the microcanonical formalism upon two fundamental thermodynamic pillars: (i) The second law of thermodynamics as formulated for quasi-static processes: $δQ/T$ is an exact differential, and (ii) the law of ideal gases: $PV=k_B NT$. The first pillar implies that entropy must be some function of the phase volume $Ω$. The second pillar singles out the logarithmic function among all possible functions. Hence the construction leads uniquely to the expression $S= k_B \ln Ω$, that is the volume entropy. As a consequence any entropy expression other than that of Gibbs, e.g., the Boltzmann entropy, can lead to inconsistencies with the two thermodynamic pillars. We illustrate this with the prototypical example of a macroscopic collection of non-interacting spins in a magnetic field, and show that the Boltzmann entropy severely fails to predict the magnetization, even in the thermodynamic limit. The uniqueness of the Gibbs entropy, as well as the demonstrated potential harm of the Boltzmann entropy, provide compelling reasons for discarding the latter at once.
We study the stochastic energetic exchanges in quantum heat engines. Due to microreversibility, these obey a fluctuation relation, called the heat engine fluctuation relation, which implies the Carnot bound: no machine can have an efficiency larger than Carnot's efficiency. The stochastic thermodynamics of a quantum heat engine (including the joint statistics of heat and work and the statistics of efficiency) is illustrated by means of an optimal two-qubit heat engine, where each qubit is coupled to a thermal bath and a two-qubit gate determines energy exchanges between the two qubits. We discuss possible solid state implementations with Cooper pair boxes and flux qubits, quantum gate operations, and fast calorimetric on-chip measurements of single stochastic events.
The charge transported when a quantum pump is adiabatically driven by time-dependent external forces in presence of dissipation is given by the line integral of a pumping field $\mathbf{F}$. We give a general expression of $\mathbf{F}$ in terms of quantum correlation functions evaluated at fixed external forces. Hence, an advantage of our method is that it transforms the original time-dependent problem into an autonomous one. Yet another advantage is that the curl of $\mathbf{F}$ gives immediate visual information about the geometric structures governing dissipative quantum pumping. This can be used in a wide range of experimental cases, including electron pumps based on quantum dots and Cooper-pair pumps based on superconducting devices. Applied to a Cooper-pair sluice, we find an intriguing dissipation-induced enhancement of charge pumping, reversals of current, and emergence of asymmetries. This geometric method thus enables one to unveil a plethora of beneficial, dissipation-assisted operation protocols.
We investigate the influences of quantum many-body effects, such as criticality and the existence of factorisation fields, in the thermodynamic cost of establishing a bonding link between two independent quantum spin chains. We provide a physical interpretation of the behavior of irreversible work spent in such process by linking the phenomenology of such quantities to the properties of the spectrum of the system
At the very foundation of the second law of thermodynamics lies the fact that no heat engine operating between two reservoires of temperatures $T_C\leq T_H$ can overperform the ideal Carnot engine: $\langle W \rangle / \langle Q_H \rangle \leq 1-T_C/T_H$. This inequality follows from an exact fluctuation relation involving the nonequilibrium work $W$ and heat exchanged with the hot bath $Q_H$. In a previous work [Sinitsyn N A, J. Phys. A: Math. Theor. {\bf 44} (2011) 405001] this fluctuation relation was obtained under the assumption that the heat engine undergoes a stochastic jump process. Here we provide the general quantum derivation, and also extend it to the case of refrigerators, in which case Carnot's statement reads: $\langle Q_C \rangle / |\langle W \rangle| \leq (T_H/T_C-1)^{-1}$.
Generalized measurements of an observable performed on a quantum system during a force protocol are investigated and conditions that guarantee the validity of the Jarzynski equality and the Crooks relation are formulated. In agreement with previous studies by Campisi {\it et al.} [M. Campisi, P. Talkner, and P. Hänggi, Phys. Rev. Lett. {\bf 105}, 140601 (2010); Phys. Rev. E {\bf 83}, 041114 (2011)], we find that these fluctuation relations are satisfied for projective measurements; however, for generalized measurements special conditions on the operators determining the measurements need to be met. For the Jarzynski equality to hold, the measurement operators of the forward protocol must be normalized in a particular way. The Crooks relation additionally entails that the backward and forward measurement operators depend on each other. Yet, quite some freedom is left as to how the two sets of operators are interrelated. This ambiguity is removed if one considers selective measurements, which are specified by a {\it joint} probability density function of work and measurement results of the considered observable. We find that the respective forward and backward joint probabilities satisfy the Crooks relation only if the measurement operators of the forward and backward protocols are the time-reversed adjoints of each other. In this case, the work probability density function {\it conditioned} on the measurement result satisfies a modified Crooks relation. The modification appears as a protocol-dependent factor that can be expressed by the information gained by the measurements during the forward and backward protocols. Finally, detailed fluctuation theorems with an arbitrary number of intervening measurements are obtained.
In [Phys. Rev. E 88, 042126 (2013)] it is stated that Tsallis distributions do not emerge from thermalization with a "bath" of finite, energy-independent, heat capacity. We report evidence for the contrary.
We study an interferometric method for the measurement of the statistics of work performed on a driven quantum system, which has been put forward recently [Dorner et al., Phys. Rev. Lett. 110 230601 (2013), Mazzola et al., Phys. Rev. Lett. 110 230602 (2013)]. The method allows replacing two projective measurements of the energy of the driven system with qubit tomography of an ancilla that is appropriately coupled to it. We highlight that this method could be employed to obtain the work statistics of closed as well as open driven system, even in the strongly dissipative regime. We then illustrate an implementation of the method in a circuit QED set-up, which allows one to experimentally obtain the work statistics of a parametrically driven harmonic oscillator. Our implementation is an extension of the original method, in which two ancilla-qubits are employed and the work statistics is retrieved through two-qubit state tomography. Our simulations demonstrate the experimental feasibility.
New quantum fluctuation relations are presented. In contrast with the the standard approach, where the initial state of the driven system is described by the (micro)canonical density matrix, here we assume that it is described by a (micro)canonical distribution of wave functions, as originally proposed by Schrödinger. While the standard fluctuation relations are based on von Neumann measurement postulate, these new fluctuation relations do not involve any quantum collapse, but involve instead a notion of work as the change in expectation of the Hamiltonian.
With this work we present two new methods for the generation of thermostated, manifestly Hamiltonian dynamics and provide corresponding illustrations. The basis for this new class of thermostats are the peculiar thermodynamics as exhibited by logarithmic oscillators. These two schemes are best suited when applied to systems with a small number of degrees of freedom.
The classical Hertz entropy is the logarithm of the volume of phase space bounded by the constant energy surface; its quantum counterpart, the quantum Hertz entropy, is $\hat S = k_B \ln \hat N$, where the quantum operator $\hat N$ specifies the number of states with energy below a given energy eigenstate. It has been recently proved that, when an isolated quantum mechanical system is driven out of equilibrium by an external driving, the change in the expectation of its quantum Hertz entropy cannot be negative, and is null for adiabatic driving. This is in full agreement with the Clausius principle. Here we test the behavior of the expectation of the quantum Hertz entropy in the case when two identical XY spin chains initially at different temperatures are quenched into a single XY chain. We observed no quantum Hertz entropy decrease. This finding further supports the statement that the quantum Hertz entropy is a proper entropy for isolated quantum systems. We further quantify how far the quenched chain is from thermal equilibrium and the temperature of the closest equilibrium.
A particle in the attractive Coulomb field has an interesting property: its specific heat is constant and negative. We show, both analytically and numerically, that when a classical Hamiltonian system stays in weak contact with one such negative specific heat object, its statistics conforms to a fat-tailed power-law distribution with power index given by $C/k_B-1$, where $k_B$ is Boltzmann constant and $C$ is the heat capacity.
An isolated classical chaotic system, when driven by the slow change of several parameters, responds with two reaction forces: geometric friction and geometric magnetism. By using the theory of quantum fluctuation relations we show that this holds true also for open quantum systems, and provide explicit expressions for those forces in this case. This extends the concept of Berry curvature to the realm of open quantum systems. We illustrate our findings by calculating the geometric magnetism of a damped charged quantum harmonic oscillator transported along a path in physical space in presence of a magnetic field and a thermal environment. We find that in this case the geometric magnetism is unaffected by the presence of the heat bath.
In response to the recent critical comment by M. Meléndez and W. G. Hoover [arXiv:1206.0188v2] on our work [M. Campisi et al., Phys. Rev. Lett. 108, 250601 (2012)], we show that their molecular dynamics simulations do not disprove our theory but in fact convincingly corroborate it.
A logarithmic oscillator (in short, log-oscillator) behaves like an ideal thermostat because of its infinite heat capacity: when it weakly couples to another system, time averages of the system observables agree with ensemble averages from a Gibbs distribution with a temperature T that is given by the strength of the logarithmic potential. The resulting equations of motion are Hamiltonian and may be implemented not only in a computer but also with real-world experiments, e.g., with cold atoms.
In response to W. G. Hoover's comment [arXiv:1204.0312v2] on our work [arXiv:1203.5968], we show explicitly that the divergence of the velocity field associated with the Nosé-Hoover equations is nonzero, implying that those equations are not volume preserving, and hence, as often stated in the literature, are not Hamiltonian. We further elucidate that the trajectories {q(t)} generated by the Nosé-Hoover equations are generally not identical to those generated by Dettmann's Hamiltonian. Dettmann's Hamiltonian produces the same trajectories as the Nosé-Hoover equations only on a specific energy shell, but not on the neighboring ones. This fact explains why the Nosé-Hoover equations are not volume preserving. The Hamiltonian that we put forward with [arXiv:1203.5968] instead produces thermostated dynamics irrespective of the energy value. The main advantage of our Hamiltonian thermostat over previous ones is that it contains kinetic energy terms that are of standard form with coordinate-independent masses and consequently is readily matched in laboratory experiments.
The recent development of the theory of fluctuation relations has led to new insights into the ever-lasting question of how irreversible behavior emerges from time-reversal symmetric microscopic dynamics. We provide an introduction to fluctuation relations, examine their relation to dissipation and discuss their impact on the arrow of time question.