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To reconstruct thermodynamics based on the microscopic laws is one of the most important unfulfilled goals of statistical physics. Here, we show that the first law and the second law for adiabatic processes are derived from an assumption that probability distributions of energy in Gibbs states satisfy large deviation, which is widely accepted as a property of thermodynamic equilibrium states. We define an adiabatic transformation as a randomized energy-preserving unitary transformations on the many-body systems and the work storage. As the second law, we show that an adiabatic transformation from a set of Gibbs states to another set of Gibbs states is possible if and only if the regularized von Neumann entropy becomes large. As the first law, we show that the energy loss of the thermodynamic systems during the adiabatic transformation is stored in the work storage as work, in the following meaning; (i) the energy of the work storage takes certain values macroscopically, in the initial state and the final state. (ii) the entropy of the work storage in the final state is macroscopically equal to the entropy of the initial state. As corollaries, our results give the principle of maximam work and the first law for the isothermal processes.
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The second law of classical thermodynamics, based on the positivity of the entropy production, only holds for deterministic processes. Therefore the Second Law in stochastic quantum thermodynamics may not hold. By making a fundamental connection between thermodynamics and information theory we will introduce a new way of defining the Second Law which holds for both deterministic classical and stochastic quantum thermodynamics. Our work incorporates information well into the Second Law and also provides a thermodynamic operational meaning for negative and positive entropy production.
The laws of thermodynamics, despite their wide range of applicability, are known to break down when systems are correlated with their environments. Here, we generalize thermodynamics to physical scenarios which allow presence of correlations, including those where strong correlations are present. We exploit the connection between information and physics, and introduce a consistent redefinition of heat dissipation by systematically accounting for the information flow from system to bath in terms of the conditional entropy. As a consequence, the formula for the Helmholtz free energy is accordingly modified. Such a remedy not only fixes the apparent violations of Landauers erasure principle and the second law due to anomalous heat flows, but also leads to a generally valid reformulation of the laws of thermodynamics. In this information-theoretic approach, correlations between system and environment store work potential. Thus, in this view, the apparent anomalous heat flows are the refrigeration processes driven by such potentials.
The efficiency of small thermal machines is typically a fluctuating quantity. We here study the efficiency large deviation function of two exemplary quantum heat engines, the harmonic oscillator and the two-level Otto cycles. While the efficiency statistics follows the universal theory of Verley et al. [Nature Commun. 5, 4721 (2014)] for nonadiabatic driving, we find that the latter framework does not apply in the adiabatic regime. We relate this unusual property to the perfect anticorrelation between work output and heat input that generically occurs in the broad class of scale-invariant adiabatic quantum Otto heat engines and suppresses thermal as well as quantum fluctuations.
According to thermodynamics, the inevitable increase of entropy allows the past to be distinguished from the future. From this perspective, any clock must incorporate an irreversible process that allows this flow of entropy to be tracked. In addition, an integral part of a clock is a clockwork, that is, a system whose purpose is to temporally concentrate the irreversible events that drive this entropic flow, thereby increasing the accuracy of the resulting clock ticks compared to counting purely random equilibration events. In this article, we formalise the task of autonomous temporal probability concentration as the inherent goal of any clockwork based on thermal gradients. Within this framework, we show that a perfect clockwork can be approximated arbitrarily well by increasing its complexity. Furthermore, we combine such an idealised clockwork model, comprised of many qubits, with an irreversible decay mechanism to showcase the ultimate thermodynamic limits to the measurement of time.
The second law of thermodynamics is discussed and reformulated from a quantum information theoretic perspective for open quantum systems using relative entropy. Specifically, the relative entropy of a quantum state with respect to equilibrium states is considered and its monotonicity property with respect to an open quantum system evolution is used to obtain second law-like inequalities. We discuss this first for generic quantum systems in contact with a thermal bath and subsequently turn to a formulation suitable for the description of local dynamics in a relativistic quantum field theory. A local version of the second law similar to the one used in relativistic fluid dynamics can be formulated with relative entropy or even relative entanglement entropy in a space-time region bounded by two light cones. We also give an outlook towards isolated quantum field theories and discuss the role of entanglement for relativistic fluid dynamics.
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