Related papers: Jensen Inequality and the Second Law
We demonstrate that the Gibbs-Shannon entropy is applicable to non-equilibrium systems of any size and boundary conditions. The change in microscopic entropy can be attributed to the stochastic nature of dynamic processes and to the…
Traditional discussions of the Second Law of Thermodynamics studied the limits of very specific types of devices, such as heat engines, chemical reactions, and molecules channeled by valves. Allahverdyan and Nieuwenhuizen (cond-mat/0110422)…
Non-equilibrium quantum thermodynamics is essential to describe new devices that operate far from the regime where the usual thermodynamical laws are obeyed. When quantum fluctuations dominate, defining and measuring work and heat, two…
In Nonequilibrium Thermodynamics and Information Theory, the relative entropy (or, KL divergence) plays a very important role. Consider a H\"older Jacobian $J$ and the Ruelle (transfer) operator $\mathcal{L}_{\log J}.$ Two equilibrium…
At very small scales, thermodynamic energy exchanges like work and heat become comparable to thermal energy of the system, which leads to unusual phenomena like the transient violations of Second Law. We explore the generic characters of…
Macroscopic thermodynamics of equilibrium is constructed for systems obeying power-law canonical distributions. With this, the connection between macroscopic thermodynamics and microscopic statistical thermodynamics is generalized. This is…
The presence of multiplicative noise can alter measurements of forces acting on nanoscopic objects. Taking into account of multiplicative noise, we derive a series of non-equilibrium thermodynamical equalities as generalization of the…
The experimental verification of the fluctuation theorem by Wang et al. is explained in terms of a simple Langevin dynamics. This implies that the entropy consuming trajectories found by Wang et al. are fluctuations generated by a random…
The Gibbs distribution universally characterizes states of thermal equilibrium. In order to extend the Gibbs distribution to non-equilibrium steady states, one must relate the self-information $\mathcal{I}(x) = -\log(P_\text{ss}(x))$ of…
This paper is a non-technical, informal presentation of our theory of the second law of thermodynamics as a law that is independent of statistical mechanics and that is derivable solely from certain simple assumptions about adiabatic…
Macroscopic cyclic heat engines have been a major motivation for the emergence of thermodynamics. In the last decade, cyclic heat engines that have large fluctuations and operate at finite time were studied within the more modern framework…
Based on the observation that the thermodynamic equilibrium free energy of an open quantum system in contact with a thermal environment can be understood as the difference between the free energy of the total system and that of the bare…
Based on recent data about the history of the Hubble factor, it is argued that the second law of thermodynamics holds at the largest scales accessible to observation. This is consistent with previous studies of the same question.
Several models of quantum open systems are known at present to violate, according to principles of the standard quantum theory of open systems, the second law of thermodynamics. Here, a new and rather trivial model of another type is…
The Jarzynski Equality relates the free energy difference between two equilibrium states of a system to the average of the work over all irreversible paths to go from one state to the other. We claim that the derivation of this equality is…
The essence of the second law of classical thermodynamics is the `entropy principle' which asserts the existence of an additive and extensive entropy function, S, that is defined for all equilibrium states of thermodynamic systems and whose…
We derive a general quantum exchange fluctuation theorem for multipartite systems with arbitrary coupling strengths by taking into account the informational contribution of the back-action of the quantum measurements, which contributes to…
We prove the second law of thermodynamics and the nonequilibirum fluctuation theorem for pure quantum states.The entire system obeys reversible unitary dynamics, where the initial state of the heat bath is not the canonical distribution but…
Deriving the laws of thermodynamics from a microscopic picture is a central quest of statistical mechanics. This tutorial focuses on the derivation of the first and second law for closed and open quantum systems far from equilibrium, where…
The Fluctuation Theorems are a group of exact relations that remain valid irrespective of how far the system has been driven away from equilibrium. Other than having practical applications, like determination of equilibrium free energy…