Work estimation and work fluctuations in the presence of non-ideal measurements

Abstract

From the perspective of quantum thermodynamics, realisable measurements cost work and result in measurement devices that are not perfectly correlated with the measured systems. We investigate the consequences for the estimation of work in non-equilibrium processes and for the fundamental structure of the work fluctuations when one assumes that the measurements are non-ideal. We show that obtaining work estimates and their statistical moments at finite work cost implies an imperfection of the estimates themselves: more accurate estimates incur higher costs. Our results provide a qualitative relation between the cost of obtaining information about work and the trustworthiness of this information. Moreover, we show that Jarzynski's equality can be maintained exactly at the expense of a correction that depends only on the system's energy scale, while the more general fluctuation relation due to Crooks no longer holds when the cost of the work estimation procedure is finite. We show that precise links between dissipation and irreversibility can be extended to the non-ideal situation.

Charging a quantum battery with linear feedback control

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Second law of thermodynamics for batteries with vacuum state

“…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].…”

Quantum thermodynamics under continuous monitoring: a general framework

“…It aims to describe work, heat and entropy production along quantum nonequilibrium processes with a special attention to genuine quantum phenomena. Paradigmatic examples include studying the thermodynamic role of quantum coherence [3][4][5][6][7] also in view of applications [8][9][10][11] , quantum correlations like entanglement [12][13][14] or discord [15][16][17] , addressing the effects of quantum measurements [18][19][20][21][22] , and exploring the link between energy and (quantum) information [23][24][25][26][27] . While most works in the field until now have focused on first-principle definitions and the behavior of average thermodynamic quantities, fluctuations are gaining increasing attention in recent years.…”