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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.
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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.
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.
One of the primary motivations of the research in the field of computation is to optimize the cost of computation. The major ingredient that a computer needs is the energy to run a process, i.e., the thermodynamic cost. The analysis of the thermodynamic cost of computation is one of the prime focuses of research. It started back since the seminal work of Landauer where it was commented that the computer spends kB T ln2 amount of energy to erase a bit of information (here T is the temperature of the system and kB represents the Boltzmanns constant). The advancement of statistical mechanics has provided us the necessary tool to understand and analyze the thermodynamic cost for the complicated processes that exist in nature, even the computation of modern computers. The advancement of physics has helped us to understand the connection of the statistical mechanics (the thermodynamics cost) with computation. Another important factor that remains a matter of concern in the field of computer science is the error correction of the error that occurs while transmitting the information through a communication channel. Here in this article, we have reviewed the progress of the thermodynamics of computation starting from Landauers principle to the latest model, which simulates the modern complex computation mechanism. After exploring the salient parts of computation in computer science theory and information theory, we have reviewed the thermodynamic cost of computation and error correction. We have also discussed about the alternative computation models that have been proposed with thermodynamically cost-efficient.
We derive a generalization of the Second Law of Thermodynamics that uses Bayesian updates to explicitly incorporate the effects of a measurement of a system at some point in its evolution. By allowing an experimenters knowledge to be updated by the measurement process, this formulation resolves a tension between the fact that the entropy of a statistical system can sometimes fluctuate downward and the information-theoretic idea that knowledge of a stochastically-evolving system degrades over time. The Bayesian Second Law can be written as $Delta H(rho_m, rho) + langle mathcal{Q}rangle_{F|m}geq 0$, where $Delta H(rho_m, rho)$ is the change in the cross entropy between the original phase-space probability distribution $rho$ and the measurement-updated distribution $rho_m$, and $langle mathcal{Q}rangle_{F|m}$ is the expectation value of a generalized heat flow out of the system. We also derive refin
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