Modern Thermodynamics

Kondepudi, Dilip K.; Prigogine, Ilya

doi:10.1002/9781118698723

Cited by 701 publications

(1,092 citation statements)

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“…The second law of thermodynamics asserts that during a time interval [0, τ ], the entropy production S tot ≥ 0 [2,25,[36][37][38]. This entropy production is that of the total system, including the surrounding medium (heat bath), and decomposes into two terms:…”

Section: Theory Second Law Of Thermodynamics In Terms Of Workmentioning

confidence: 99%

Direct measurement of weakly nonequilibrium system entropy is consistent with Gibbs–Shannon form

Gavrilov

Chétrite

Bechhoefer

2017

Proc. Natl. Acad. Sci. U.S.A.

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Stochastic thermodynamics extends classical thermodynamics to small systems in contact with one or more heat baths. It can account for the effects of thermal fluctuations and describe systems far from thermodynamic equilibrium. A basic assumption is that the expression for Shannon entropy is the appropriate description for the entropy of a nonequilibrium system in such a setting. Here, for the first time, we measure experimentally this function. Our system is a micron-scale colloidal particle in water, in a virtual double-well potential created by a feedback trap. We measure the work to erase a fraction of a bit of information and show that it is bounded by the Shannon entropy for a twostate system. Further, by measuring directly the reversibility of slow protocols, we can distinguish unambiguously between protocols that can and cannot reach the expected thermodynamic bounds. INTRODUCTIONBeginning with the foundational work of Clausius, Maxwell, and Boltzmann in the 19th c., the concept of entropy has played a key role in thermodynamics. Yet, despite its importance, entropy is an elusive concept [1][2][3][4][5][6][7][8], with no unique definition; rather, the appropriate definition of entropy depends on the scale, relevant thermodynamic variables, and nature of the system, with ongoing debate existing over the proper definition even for equilibrium cases [9]. Moreover, entropy has not been directly measured but is rather inferred from other quantities, such as the integral of the specific heat divided by temperature. Here, by measuring the work required to erase a fraction of a bit of information, we isolate directly the change in entropy in an open nonequilibrium system, showing that it is compatible with the functional form proposed by Gibbs and Shannon, giving it a physical meaning in this context. Knowing the relevant form of entropy is crucial for efforts to extend thermodynamics to systems out of equilibrium.For a continuous classical system whose state in phase space x is distributed as the probability density function ρ(x), the Gibbs-Shannon entropy is [10,11] where k B is Boltzmann's constant. For quantum systems, von Neumann introduced, in 1927, the corresponding expression in terms of the density matrix [12]. Historically, the system in Eq. 1 has typically been assumed to be in thermal equilibrium. * email: johnb@sfu.caThe physical relevance of Eq. 1 for a nonequilibrium distribution ρ(x) has often been questioned (e.g., [13][14][15][16][17]). One concern is that S is constant on an isolated Hamiltonian system and can change only when evaluated on subsystems, such as those picked out by coarse graining. With many ways to choose subsystems or to coarse grain, is the associated notion of irreversibility intrinsic to the description of the system?In another approach to entropy, advanced in the context of communication and information theory, Shannon [11,18] proved that, up to a multiplicative constant, S is the only possible function satisfying three intuitive axioms. Alternatively, one can start from an...

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Section: Theory Second Law Of Thermodynamics In Terms Of Workmentioning

confidence: 99%

Direct measurement of weakly nonequilibrium system entropy is consistent with Gibbs–Shannon form

Gavrilov

Chétrite

Bechhoefer

2017

Proc. Natl. Acad. Sci. U.S.A.

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“…In this paper we clarify the role of nonequilibrium quantum reservoirs via the analysis of entropy production, one of the most fundamental concepts in nonequilibrium thermodynamics, which quantifies the degree of irreversibility of a dynamical evolution [30]. For a quantum system relaxing in a thermal reservoir in equilibrium at inverse temperature β = 1/k B T , it simply reads [31][32][33] = S − βQ 0,…”

Section: Introductionmentioning

confidence: 99%

Entropy production and thermodynamic power of the squeezed thermal reservoir

et al. 2016

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We analyze the entropy production and the maximal extractable work from a squeezed thermal reservoir. The nonequilibrium quantum nature of the reservoir induces an entropy transfer with a coherent contribution while modifying its thermal part, allowing work extraction from a single reservoir, as well as great improvements in power and efficiency for quantum heat engines. Introducing a modified quantum Otto cycle, our approach fully characterizes operational regimes forbidden in the standard case, such as refrigeration and work extraction at the same time, accompanied by efficiencies equal to unity.

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“…In this respect, notice that (13) and (14) can be satisfied only for a single energy value. This mechanism is called reversible cooling at the contacts.…”

Section: T Hmentioning

confidence: 99%

“…In subsequent sections, we will discuss how the novel solar cells sprout from this trunk as branches depending on the hypotheses made. For that, we will assume local equilibrium thermodynamics valid so that the description of the systems by thermodynamic variables such as temperature and electrochemical potentials still makes sense even in nonequilibrium [13]- [15]. The process will also lead us to better understand why the relationships between electron and hole quasi-Fermi levels, cell output voltage, and emitted photons electrochemical potentials are apparently so different from one cell to another.…”

Section: Introductionmentioning

confidence: 99%

Electrochemical Potentials (Quasi-Fermi Levels) and the Operation of Hot-Carrier, Impact-Ionization, and Intermediate-Band Solar Cells

Martı́

Ĺuque

2013

IEEE J. Photovoltaics

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Abstract-In the framework of the so-called third generation solar cells, three main concepts have been proposed in order to exceed the limiting efficiency of single-gap solar cells: the hot-carrier solar cell, the impact-ionization or multiple-exciton-generation solar cell, and the intermediate-band solar cell. At first sight, the three concepts are different, but in this paper, we illustrate how all these concepts, including the single-gap solar cell, share a common trunk that we call "core photovoltaic material." We demonstrate that each one of these next-generation concepts differentiates in fact from this trunk depending on the hypotheses that are made about the physical principles governing the electron electrochemical potentials. In the process, we also clarify the differences between electron, phonon, and photon chemical potentials (the three fundamental particles involved in the operation of the solar cell). The in-depth discussion of the physics involved about the operation of these cells also provides new insights about the operation of these cells.

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Modern Thermodynamics

Cited by 701 publications

References 0 publications

Direct measurement of weakly nonequilibrium system entropy is consistent with Gibbs–Shannon form

Direct measurement of weakly nonequilibrium system entropy is consistent with Gibbs–Shannon form

Entropy production and thermodynamic power of the squeezed thermal reservoir

Electrochemical Potentials (Quasi-Fermi Levels) and the Operation of Hot-Carrier, Impact-Ionization, and Intermediate-Band Solar Cells

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