Let a general quantum many-body system at a low temperature adiabatically cross through the vicinity of the system's quantum critical point. We show that the system's temperature is significantly suppressed due to both the entropy majorization theorem in quantum information science and the entropy conservation law in adiabatic processes. We take the one-dimensional transverse-field Ising model and spinless fermion system as concrete examples to show that the inverse temperature might become divergent around their critical points. Since the temperature is a measurable quantity in experiments, our work, therefore, provides a practicable proposal to detect quantum phase transitions.
We compare the roles of fidelity and entanglement in characterizing renormalization group flows and quantum phase transitions. It turns out that the scaling parameter extracted from fidelity for different ground states succeeds to capture nontrivial information including stable and unstable fixed points, whereas the von Neumann entropy as a bipartite entanglement measure (or equivalently, majorization relations satisfied by the spectra of the reduced density matrix along renormalization group flows) often fails, as far as the intrinsic irreversibility-information loss along renormalization gro…
In these decades, it has been revealed that there is rich information-theoretic structure in thermodynamics of out-of-equilibrium systems in both the classical and quantum regimes. This has led to the fruitful interplay among statistical physics, quantum information theory, and mathematical theories including matrix analysis and asymptotic probability theory. The main purpose of this book is to clarify how information theory works behind thermodynamics and to shed modern light on it. We focus on both of purely information-theoretic concepts and their physical implications: We present self-cont…
We present our numerical study on quantum thermodynamics of the resonant level model subjected to non-equilibrium condition as well as external driving. Following our previous work on non-equilibrium quantum thermodynamics (Phys. Rev. B 101, 184304 [2020]), we expand the density operator into a series of power in the driving speed, where we can determine the non-adiabatic thermodynamic quantities. Particularly, we calculate the non-equilibrium entropy production rate as well as higher order non-adiabatic corrections to the energy and/or population. In the limit of weak system-bath coupling, ou…
By applying adiabatic theorem to a Markovian system, we calculate the adiabatic and diabatic entropy changes along a path. As well known, the total path entropy change is separated into two parts, system and environment entropy changes, $ΔS_{tot} = ΔS_{sys} + ΔS_{env}$. The environment entropy change, $ΔS_{env}$, is divided again into two parts, an adiabatic contribution due to work, $ΔS_{\mathcal{W}}$, and a diabatic contributions due to heat, $ΔS_{\mathcal{Q}}$. In an adiabatic process, total path entropy change is same with the adiabatic path entropy change, $ΔS_{A}$, which is given by sum …
The spin-1/2 Ising octahedron and dodecahedron with a unique antiferromagnetic interaction display an outstanding magnetization jump at zero magnetic field, which consequently leads to a giant magnetocaloric effect during the adiabatic demagnetization. In the present work we report temperature dependences of two basic magnetocaloric response functions: the isothermal entropy change and the adiabatic change of temperature. It is shown that the Ising octahedron and dodecahedron generally exhibit a large negative isothermal entropy change upon increasing of the magnetic field, which serves in evi…
We analyze the production of entropy along non-equilibrium processes in quantum systems coupled to generic environments. First, we show that the entropy production due to final measurements and the loss of correlations obeys a fluctuation theorem in detailed and integral forms. Second, we discuss the decomposition of the entropy production into two positive contributions, adiabatic and non-adiabatic, based on the existence of invariant states of the local dynamics. Fluctuation theorems for both contributions hold only for evolutions verifying a specific condition of quantum origin. We illustra…
Specific heat and entropy are relevant thermodynamic properties, which may be used as macroscopic probes to microscopic properties of materials under ambient conditions and under high applied fields. However, the measurement of specific heat under intense external fields can be a challenging task, as well as to obtain the entropy in the same conditions. Here, we describe a method to obtain high-field specific heat and entropy from measurements of specific heat under ambient conditions and direct temperature change induced by adiabatic field changes. We derive straightforward thermodynamic equa…
We study the nature of currents, input energy and entropy production in different types of adiabatically rocked ratchets using the method of stochastic energetics. The currents exhibit a peak as a function of noise strength. We show that there is no underlying resonance or synchronisation phenomena in the dynamics of the particle with these current peaks. This follows from the analysis of energy loss in the medium. We also show that the maxima seen in current as well as the total entropy production are not directly correlated.
How the thermodynamic entropy $S_{TD}$ is related to the Boltzmann entropy $S_{B}$ has been one of the central issues since the beginning of statistical mechanics. Today, it is believed that the thermodynamic entropy $S_{TD}$ is equal to a function $\tilde{S}_{B}$ that is defined by regularizing the Boltzman entropy in order to ensure extensivity. However, it is not known whether $\tilde{S}_{B}$ completely determines the possibility of a macroscopic adiabatic transformation in the same way as $S_{TD}$ does. In this paper, by formulating the possibility of a macroscopic adiabatic transformation…
Entropy has become increasingly central to characterize, understand and even guide assembly, self-organization and phase transition processes. In this work, we build on the analogous role of partition functions (or free energies) in isothermal ensembles and that of entropy in adiabatic ensembles. In particular, we show that the grand-isobaric adiabatic $(μ,P,R)$ ensemble, or Ray ensemble, provides a direct route to determine the entropy. This allows us to follow the variations of entropy with the thermodynamic conditions and thus to explore phase transitions. We test this approach by carrying …
This short article was submitted to Nature Physics as a Correspondence. The intention was to provide a brief albeit significant criticism of the work of J. Dunkel and S. Hilbert, \textit{Consistent Thermostatistics Forbids Negative Absolute Temperatures}, Nature Physics \textbf{10}, (2014). The respected editor decided not to publish the Correspondence. We have therefore decided to submit the paper to arXiv. Comments/criticisms are welcomed, particularly from the authors of the mentioned paper.
Attempts to establish microcanonical entropy as an adiabatic invariant date back to works of Gibbs and Hertz. More recently, a consistency relation based on adiabatic invariance has been used to argue for the validity of Gibbs (volume) entropy over Boltzmann (surface) entropy. Such consistency relation equates derivatives of thermodynamic entropy to ensemble average of the corresponding quantity in micro-state space (phase space or Hilbert space). In this work we propose to re-examine such a consistency relation when the number of particles ($N$) is considered as the independent thermodynamic …
A unified framework to describe the adiabatic class of ensembles in the generalized statistical mechanics based on Schwammle-Tsallis two parameter (q, q') entropy is proposed. The generalized form of the equipartition theorem, virial theorem and the adiabatic theorem are derived. Each member of the class of ensembles is illustrated using the classical nonrelativistic ideal gas and we observe that the heat functions could be written in terms of the Lambert's W-function in the large N limit. In the microcanonical ensemble we study the effect of gravitational field on classical nonrelativistic id…
A typical strategy of realizing an adiabatic change of a many-particle system is to vary parameters very slowly on a time scale $t_\text{r}$ much larger than intrinsic equilibration time scales. In the ideal case of adiabatic state preparation, $t_\text{r} \to \infty$, the entropy production vanishes. In systems with conservation laws, the approach to the adiabatic limit is hampered by hydrodynamic long-time tails, arising from the algebraically slow relaxation of hydrodynamic fluctuations. We argue that the entropy production $ΔS$ of a diffusive system at finite temperature in one or two dime…
The entropy change that occurs upon mixing two fluids has remained an intriguing topic since the dawn of statistical mechanics. In this work, we generalize the grand-isobaric ensemble to mixtures, and develop a Monte Carlo algorithm for the rapid determination of entropy in these systems. A key advantage of adiabatic ensembles is the direct connection they provide with entropy. Here, we show how the entropy of a binary mixture A-B can be readily obtained in the adiabatic grand-isobaric $(μ_{\text{A}}$, $μ_{\text{B}}, P, R)$ ensemble, in which $μ_{\text{A}}$ and $μ_{\text{B}}$ denote the chemic…
We extend the definition of non-adiabatic entropy production given for Markovian systems in [M. Esposito and C. Van den Broeck, Phys. Rev. Lett. 104 090601, (2010)], to arbitrary non-Markov ergodic dynamics. We also introduce a notion of stability characterizing non-Markovianity. For stable non-Markovian systems, the non-adiabatic entropy production satisfies an integral fluctuation theorem, leading to the second law of thermodynamics for transitions between non-equilibrium steady-states. This quantity can also be written as a sum of products of generalized fluxes and forces, thus being suitab…
We study adaptive control of classical ergodic Hamiltonian systems, where the controlling parameter varies slowly in time and is influenced by system's state (feedback). An effective adiabatic description is obtained for slow variables of the system. A general limit on the feedback induced negative entropy production is uncovered. It relates the quickest negentropy production to fluctuations of the control Hamiltonian. The method deals efficiently with the entropy-information trade off.
The total entropy production of a trajectory can be split into an adiabatic and a non-adiabatic contribution, deriving respectively from the breaking of detailed balance via nonequilibrium boundary conditions or by external driving. We show that each of them, the total, the adiabatic and the non-adiabatic trajectory entropy, separately satisfies a detailed fluctuation theorem.
We experimentally realize quasistatic adiabatic processes using a single optically-trapped micro- sphere immersed in water whose effective temperature is controlled by an external random electric field. A full energetic characterization of adiabatic processes that preserve either the position dis- tribution or the full phase space volume is presented. We show that only in the latter case the exchanged heat and the change in the entropy of the particle vanish when averaging over many repetitions. We provide analytical expressions for the distributions of the fluctuating heat and en- tropy, whic…
I employ the van der Waals theory of Baus and coworkers to analyze the fast, adiabatic decay of a supercooled liquid in a closed vessel with which the solidification process usually starts. By imposing a further constraint on either the system volume or pressure, I use the maximum-entropy method to quantify the fraction of liquid that is transformed into solid as a function of undercooling and of the amount of a foreign gas that could possibly be also present in the test tube. Upon looking at the implications of thermal and mechanical insulation for the energy cost of forming a solid droplet w…
We investigate entropy production in finitely slow transitions between nonequilibrium steady states in Markov jump processes using the improved adiabatic approximation method proposed by Takahashi, Fujii, Hino and Hayakawa [1]. This method provides systematic improvement of the adiabatic approximation on infinitely slow transitions from which we obtain nonadiabatic corrections and has a close relationship with the slow driving perturbation [2, 3]. We analyze two types of excess entropy production of Sagawa and Hayakawa [4] and Hatano and Sasa [5] as examples, and confirm that the leading adiab…
In earlier work we presented a foundation for the Second Law of Classical Thermodynamics in terms of the Entropy Principle. More precisely, we provided an empirically accessible axiomatic derivation of an entropy function defined on all equilibrium states of all systems that has the appropriate additivity and scaling properties and whose increase is a necessary and sufficient condition for an adiabatic process between two states to be possible. Here, after a brief review of this approach, we address the question of defining entropy for non-equilibrium states. Our conclusion is that it is gener…
We present a novel numerical approach to track the response of a quantum system to an external perturbation that is progressively switched-on. The method is applied, within the framework of the density matrix renormalization group technique, to track current-carrying states of interacting fermions in one dimension and in presence of an Aharonov-Bohm magnetic flux. This protocol allows us to access highly excited states. We also discuss the connection with the entanglement entropy of these excited states.
Thermodynamics teaches that if a system initially off-equilibrium is coupled to work sources, the maximum work that it may yield is governed by its energy and entropy. For finite systems this bound is usually not reachable. The maximum extractable work compatible with quantum mechanics (``ergotropy'') is derived and expressed in terms of the density matrix and the Hamiltonian. It is related to the property of majorization: more major states can provide more work. Scenarios of work extraction that contrast the thermodynamic intuition are discussed, e.g. a state with larger entropy than another …
Clarifying the impact of quantumness in the operation and properties of thermal machines represents a major challenge. Here we envisage a toy model acting either as an information-driven fridge or as heat-powered information eraser in which coherences can be naturally introduced in by means of squeezed thermal reservoirs. We study the validity of the transient entropy production fluctuation theorem in the model with and without squeezing as well as its decomposition into adiabatic and non-adiabatic contributions. Squeezing modifies fluctuations and introduces extra mechanisms of entropy exchan…
It is proved here that, as a consequence of the unitary quantum evolution, the expectation value of a properly defined quantum entropy operator (as opposed to the non-evolving von Neumann entropy) can only increase during non adiabatic transformations and remains constant during adiabatic ones. Thus Clausius formulation of the second law is established as a theorem in quantum mechanics, in a way that is equivalent to the previously established formulation in terms of minimal work principle [A. E. Allahverdyan and T. M. Nieuwenhuizen, Phys. Rev. E 71, 046107 (2005)]. The corresponding Quantum M…
We address the calculation of microcanonical reaction rates for processes involving significant nuclear quantum effects using ring-polymer molecular dynamics (RPMD), both with and without electronically non-adiabatic transitions. After illustrating the shortcomings of the naive free-particle direct-shooting method, in which the temperature of the internal ring-polymer modes is set to the translational energy scale, we investigate alternative strategies based on the expression for the microcanonical rate in terms of the inverse Laplace transform of the thermal reaction rate. It is shown that si…
The total entropy production generated by the dynamics of an externally driven systems exchanging energy and matter with multiple reservoirs and described by a master equation is expressed as the sum of three contributions, each corresponding to a distinct mechanism for bringing the system out of equilibrium: nonequilibrium initial conditions, external driving, and breaking of detailed balance. We derive three integral fluctuation theorems (FTs) for these contributions and show that they lead to the following universal inequality: an arbitrary nonequilibrium transformation always produces a ch…
Carnot's four-part ideal-gas cycle includes both isothermal and adiabatic expansions and compressions. Analyzing this cycle provides the fundamental basis for statistical thermodynamics. We explore the cycle here from a pedagogical view in order to promote understanding of the macroscopic thermodynamic entropy, the state function associated with thermal energy changes. From the alternative microscopic viewpoint the Hamiltonian ${\cal H}(q,p)$ is the energy and entropy is the (logarithm of the) phase-space volume $Ω$ associated with a macroscopic state. We apply two novel forms of Hamiltonian m…
This article is a short version of a longer article to appear in Physics Reports (cond-mat/9708200). The essential postulates of classical thermodynamics are formulated, from which the second law is deduced as the principle of increase of entropy in irreversible adiabatic processes that take one equilibrium state to another. The entropy constructed here is defined only for equilibrium states and no attempt is made to define it otherwise. Statistical mechanics does not enter these considerations. One of the main concepts that makes everything work is the comparison principle (which, in essence,…
