Related papers: Compactified Time and likely Entropy -- World Insi…
We prove a lower bound on the relative entropy between two finite-dimensional states in terms of their entropy difference and the dimension of the underlying space. The inequality is tight in the sense that equality can be attained for any…
Firstly, we calculate quantitatively decrease of entropy by the known formulas in the ordering phenomena and nucleation of thermodynamics of microstructure. They show again that a necessary condition of decrease of entropy in isolated…
Based on Newton's laws reformulated in the Hamiltonian dynamics combined with statistical mechanics, we formulate a statistical mechanical theory supporting the hypothesis of a closed oscillating universe. We find that the behaviour of the…
A recently proposed quantum mechanical criterion `concavity of energy' for the second law of thermodynamics is studied also for classical particle systems confined in a bounded region by a potential with a time-dependent coupling constant.…
The entropy of a thermally isolated system should not decrease after a quench or external driving. For a classical system following Hamiltonian dynamics, we show how this statement emerges for a large system in the sense that the extensive…
A version of the second law of thermodynamics states that one cannot lower the energy of an isolated system by a cyclic operation. We prove this law without introducing statistical ensembles and by resorting only to quantum mechanics. We…
In a macroscopic (quantum or classical) Hamiltonian system, we prove the second law of thermodynamics in the forms of the minimum work principle and the law of entropy increase, under the assumption that the initial state is described by a…
Quantum mechanics is derived as an application of the method of maximum entropy. No appeal is made to any underlying classical action principle whether deterministic or stochastic. Instead, the basic assumption is that in addition to the…
Quantum many-body states that frequently appear in physics often obey an entropy scaling law, meaning that an entanglement entropy of a subsystem can be expressed as a sum of terms that scale linearly with its volume and area, plus a…
Entropy is the distinguishing and most important concept of our efforts to understand and regularize our observations of a very large class of natural phenomena, and yet, it is one of the most contentious concepts of physics. In this…
In the framework of Lindblad theory for open quantum systems, we calculate the entropy of a damped quantum harmonic oscillator which is initially in a quasi-free state. The maximally predictable states are identified as those states…
We seek here to unify the second law of thermodynamics with the other laws, or at least to put up a law behind the second law of thermodynamics. Assuming no fine tuning, concretely by a random Hamiltonian, we argue just from equations of…
We show how the dependence of phase space volume $\Omega(N)$ of a classical system on its size $N$ uniquely determines its extensive entropy. We give a concise criterion when this entropy is not of Boltzmann-Gibbs type but has to assume a…
The second law of thermodynamics states that entropy production in macroscopic systems is non-negative, reaching zero only at thermodynamic equilibrium. As a corollary, this implies that the state trajectory of macroscopic systems is…
Time is a parameter playing a central role in our most fundamental modeling of natural laws. Relativity theory shows that the comparison of times measured by different clocks depends on their relative motions and on the strength of the…
The second law of thermodynamics states that the entropy of an isolated system is almost always increasing. We propose combinatorial formalizations of the second law and explore their conditions of possibilities.
The volume of phase space may grow super-exponentially ("explosively") with the number of degrees of freedom for certain types of complex systems such as those encountered in biology and neuroscience, where components interact and create…
A major part of the many thermally driven processes in our natural environment as well as in engineering solutions of Carnot-type machinery is based on the second law of thermodynamics (or principle of entropy increase). An interesting link…
We introduce the notion of time reversal in open quantum systems as represented by linear quantum operations, and a related generalization of classical entropy production in the environment. This functional is the ratio of the probability…
Applying the theory of self-adjoint extensions of Hermitian operators to Koopman von Neumann classical mechanics, the most general set of probability distributions is found for which entropy is conserved by Hamiltonian evolution. A new…