Maximum one-shot dissipated work from Renyi divergences

Traditional thermodynamics governs the behaviour of large systems that evolve between states of thermal equilibrium. For these large systems, the mean values of thermodynamic quantities (such as work, heat and entropy) provide a good characterisation of the process. Conversely, there is ever-increasing interest in the thermal behaviour of systems that evolve quickly and far from equilibrium, and that are too small for their behaviour to be well-described by mean values. Two m...

Two approaches to small-scale and quantum thermodynamics are fluctuation relations and one-shot statistical mechanics. Fluctuation relations (such as Crooks' Theorem and Jarzynski's Equality) relate nonequilibrium behaviors to equilibrium quantities such as free energy. One-shot statistical mechanics involves statements about every run of an experiment, not just about averages over trials. We investigate the relation between the two approaches. We show that both approaches ...

In this paper, we establish a general relation which directly links the dissipated work done on a system driven arbitrarily far from equilibrium, a fundamental quantity in thermodynamics, and the R\'{e}nyi divergences, a fundamental concept in information theory. Specifically, we find that the generating function of the dissipated work under an arbitrary time-dependent driving process is related to the R\'{e}nyi divergences between a non-equilibrium state in the driven proces...

In this work, we establish an exact relation which connects the heat exchange between two systems initialized in their thermodynamic equilibrium states at different temperatures and the R\'{e}nyi divergences between the initial thermodynamic equilibrium state and the final non-equilibrium state of the total system. The relation tells us that the various moments of the heat statistics are determined by the Renyi divergences between the initial equilibrium state and the final n...

The work content of non-equilibrium systems in relation to a heat bath is often analyzed in terms of expectation values of an underlying random work variable. However, we show that when optimizing the expectation value of the extracted work, the resulting extraction process is subject to intrinsic fluctuations, uniquely determined by the Hamiltonian and the initial distribution of the system. These fluctuations can be of the same order as the expected work content per se, in ...

Reducing work fluctuation and dissipation in heat engines or, more generally, information heat engines that perform feedback control is vital to maximize their efficiency. The same problem arises when we attempt to maximize the efficiency of a given thermodynamic task that undergoes nonequilibrium processes for arbitrary initial and final states. We find that the most general trade-off relation between work fluctuation and dissipation applicable to arbitrary nonequilibrium pr...

In the standard framework of thermodynamics the work produced or consumed in a process is a random variable whose average value is bounded by the change in the free energy of the system. This work is calculated without regard for the size of its fluctuations. We find that in some processes, such as reversible cooling, the fluctuations of the work can diverge. Small or fragile thermal machines may be unable to cope with large fluctuations. Hence, with the present focus on nano...

Conventional statistical mechanics describes large systems and averages over many particles or over many trials. But work, heat, and entropy impact the small scales that experimentalists can increasingly control, e.g., in single-molecule experiments. The statistical mechanics of small scales has been quantified with two toolkits developed in quantum information theory: resource theories and one-shot information theory. The field has boomed recently, but the theorems amassed h...

There has been an increasing interest in the quantification of nearly deterministic work extraction from a finite number of copies of microscopic particles in finite time. This paradigm, so called single-shot epsilon-deterministic work extraction, considers processes with small failure probabilities. However, the resulting fluctuations in the extracted work entailed by this failure probability have not been studied before. In the standard thermodynamics paradigm fluctuation t...

Physical systems powering motion or creating structure in a fixed amount of time dissipate energy and produce entropy. Here, we derive speed limits on dissipation from the classical, chaotic dynamics of many-particle systems: the inverse of the entropy irreversibly produced bounds the time to execute a physical process for deterministic systems out of equilibrium, $\Delta t\geq k_B/\bar s_i$. We relate this statistical-mechanical speed limit on the mean entropy rate to determ...