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Register a new userGeneralized Laws of Thermodynamics in the Presence of Correlations
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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.
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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.
The holographic principle states that on a fundamental level the information content of a region should depend on its surface area rather than on its volume. This counterintuitive idea which has its roots in the nonextensive nature of black-hole entropy serves as a guiding principle in the search for the fundamental laws of Planck-scale physics. In this paper we show that a similar phenomenon emerges from the established laws of classical and quantum physics: the information contained in part of a system in thermal equilibrium obeys an area law. While the maximal information per unit area depends classically only on the number of microscopic degrees of freedom, it may diverge as the inverse temperature in quantum systems. A rigorous relation between area laws and correlations is established and their explicit behavior is revealed for a large class of quantum many-body states beyond equilibrium systems.
We analyze the role of indirect quantum measurements in work extraction from quantum systems in nonequilibrium states. In particular, we focus on the work that can be obtained by exploiting the correlations shared between the system of interest and an additional ancilla, where measurement backaction introduces a nontrivial thermodynamic tradeoff. We present optimal state-dependent protocols for extracting work from both classical and quantum correlations, the latter being measured by discord. We show that, while the work content of classical correlations can be fully extracted by performing local operations on the system of interest, the amount of work related to quantum discord requires a specific driving protocol that includes interaction between system and ancilla.
We consider locally thermal states (for two qubits) with certain amount of quantum entanglement present between them. Unlike previous protocols we show how work can be extracted by performing local unitary operations on this state by allowing those two qubits to interact with thermal baths of different temperatures, thereby gradually removing the entanglement between them till they reach a direct product state. Also we demonstrate that, further work can be extracted from this direct product state by performing global unitary operation, thereby establishing that work can be extracted from a system composed of locally thermal subsystems even after removing quantum correlations between them if the subsystems are thermalized at different temperatures. Also we show that even if we consider a initial state where there is no entanglement between the two qubits, we can also extract work locally using our method.
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.
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