Detailed Fluctuation Theorems: A Unifying Perspective

We study the statistics of heat exchange of a quantum system that collides sequentially with an arbitrary number of ancillas. This can describe, for instance, an accelerated particle going through a bubble chamber. Unlike other approaches in the literature, our focus is on the joint probability distribution that heat Q 1 is exchanged with ancilla 1, heat Q 2 is exchanged with ancilla 2, and so on. This allows us to address questions concerning the correlations between the collisional events. For instance, if in a given realization a large amount of heat is exchanged with the first ancilla, then there is a natural tendency for the second exchange to be smaller. The joint distribution is found to satisfy a Fluctuation theorem of the Jarzynski–Wójcik type. Rather surprisingly, this fluctuation theorem links the statistics of multiple collisions with that of independent single collisions, even though the heat exchanges are statistically correlated.

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“…Beyond that, a generalization of the detailed FT to multiple reservoirs has also being obtained before, e.g., in Ref. [ 25 ].…”

Section: Joint Fluctuation Theorem For Heat Exchangementioning

confidence: 84%

Joint Fluctuation Theorems for Sequential Heat Exchange

Santos

Timpanaro

Landi

2020

Entropy

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“…Notice that operator M , its eigenvalues and its mean value

for a given state

, that we first termed “nonequilibrium Massieu operator” in References [ 62 , 94 , 107 ], differ substantially from the “nonequilibrium Massieu potentials” defined recently in References [ 108 , 109 ]. Their nonequilibrium Massieu construct is defined by the difference between the entropy and a linear combination of the conserved properties, with coefficients that are weighted averages of the fixed temperatures and other entropic potentials of the reservoirs interacting with the system.…”

Section: Example Steepest-entropy-ascent Master Equation For Consmentioning

confidence: 99%

Time–Energy and Time–Entropy Uncertainty Relations in Nonequilibrium Quantum Thermodynamics under Steepest-Entropy-Ascent Nonlinear Master Equations

Beretta

2019

Entropy

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In the domain of nondissipative unitary Hamiltonian dynamics, the well-known Mandelstam-Tamm-Messiah time-energy uncertainty relation τF ∆H ≥h/2 provides a general lower bound to the characteristic time τF = ∆F /|d F /dt| with which the mean value of a generic quantum observable F can change with respect to the width ∆F of its uncertainty distribution (square root of F fluctuations). A useful practical consequence is that in unitary dynamics the states with longer lifetimes are those with smaller energy uncertainty ∆H (square root of energy fluctuations). Here we show that when unitary evolution is complemented with a steepest-entropy-ascent model of dissipation, the resulting nonlinear master equation entails that these lower bounds get modified and depend also on the entropy uncertainty ∆S (square root of entropy fluctuations). For example, we obtain the time-energy-and-time-entropy uncertainty relation (2τF ∆H /h) 2 + (τF ∆S/kBτ ) 2 ≥ 1 where τ is a characteristic dissipation time functional that for each given state defines the strength of the nonunitary, steepest-entropy-ascent part of the assumed master equation. For purely dissipative dynamics this reduces to the time-entropy uncertainty relation τF ∆S ≥ kBτ , meaning that the nonequilibrium dissipative states with longer lifetime are those with smaller entropy uncertainty ∆S.

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“…In order to take full advantage of these techniques it is crucial to understand how thermodynamic laws translate into the non-equilibrium domain, where fluctuations of thermodynamic quantities begin to play a significant role and averaged quantities are no longer enough to characterize their thermodynamic behaviour. This motivates extending thermodynamic framework to systems driven out of equilibrium, a setting which has been extensively studied in the recent literature [7][8][9][10][11][12][13][14][15].…”

Section: Introductionmentioning

confidence: 99%

Second law of thermodynamics for batteries with vacuum state

Lipka-Bartosik

Mazurek

Horodecki

2021

Quantum

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In stochastic thermodynamics work is a random variable whose average is bounded by the change in the free energy of the system. In most treatments, however, the work reservoir that absorbs this change is either tacitly assumed or modelled using unphysical systems with unbounded Hamiltonians (i.e. the ideal weight). In this work we describe the consequences of introducing the ground state of the battery and hence — of breaking its translational symmetry. The most striking consequence of this shift is the fact that the Jarzynski identity is replaced by a family of inequalities. Using these inequalities we obtain corrections to the second law of thermodynamics which vanish exponentially with the distance of the initial state of the battery to the bottom of its spectrum. Finally, we study an exemplary thermal operation which realizes the approximate Landauer erasure and demonstrate the consequences which arise when the ground state of the battery is explicitly introduced. In particular, we show that occupation of the vacuum state of any physical battery sets a lower bound on fluctuations of work, while batteries without vacuum state allow for fluctuation-free erasure.

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Detailed Fluctuation Theorems: A Unifying Perspective

Cited by 40 publications

References 46 publications

Joint Fluctuation Theorems for Sequential Heat Exchange

Joint Fluctuation Theorems for Sequential Heat Exchange

Time–Energy and Time–Entropy Uncertainty Relations in Nonequilibrium Quantum Thermodynamics under Steepest-Entropy-Ascent Nonlinear Master Equations

Second law of thermodynamics for batteries with vacuum state

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