Related papers: When you can't count, sample! Computable entropies…
In this paper, we review the concept of entropy in connection with the description of quantum unstable systems. We revise the conventional definition of entropy due to Boltzmann and extend it so as to include the presence of complex-energy…
Our previous works have shown the statistical mechanics of self-gravitating system. In this paper, we will show its thermodynamics and compare our results with observations and simulations. We propose that our statistical mechanics can be…
There is no compelling reason imposing that the methods of statistical mechanics should be restricted to the dynamical systems which follow the usual Boltzmann-Gibbs prescriptions. More specifically, ubiquitous natural and artificial…
The foundations of statistical mechanics, namely how equilibrium hypothesis emerges microscopically from quantum theory, is explored through investigating the environment-induced quantum decoherence processes. Based on the recent results on…
The postulates of thermodynamics were originally formulated for macroscopic systems. They lead to the definition of the entropy, which, for a homogeneous system, is a homogeneous function of order one in the extensive variables and is…
The concept of entropy connects the number of possible configurations with the number of variables in large stochastic systems. Independent or weakly interacting variables render the number of configurations scale exponentially with the…
Entropy production in stochastic mechanical systems is examined here with strict bounds on its rate. Stochastic mechanical systems include pure diffusions in Euclidean space or on Lie groups, as well as systems evolving on phase space for…
Many physicists think that the maximum entropy formalism is a straightforward application of Bayesian statistical ideas to statistical mechanics. Some even say that statistical mechanics is just the general Bayesian logic of inductive…
We provide a general macrostatistical formulation of nonequilibrium steady states of reservoir driven quantum systems. This formulation is centred on the large scale properties of the locally conserved hydrodynamical observables, and our…
Lack of knowledge about the detailed many-particle motion on the microscopic scale is a key issue in any theoretical description of a macroscopic experiment. For systems at or close to thermal equilibrium, statistical mechanics provides a…
Plasmas and other systems with long-range interactions are commonly found in non-equilibrium steady states that are outside traditional Boltzmann-Gibbs statistics, but can be described using generalized statistical mechanics frameworks such…
Time-reversal symmetry breaking and entropy production are universal features of nonequilibrium phenomena. Despite its importance in the physics of active and living systems, the entropy production of systems with many degrees of freedom…
The paper moves a step towards the full integration of statistical mechanics and information theory. Starting from the assumption that the thermodynamical system is composed by particles whose quantized energies can be modelled as…
Randomness is viewed through an analogy between a physical quantity, density of gas, and a mathematical construct -- probability density. Boltzmann's deduction of equilibrium distribution of ideal gas placed in an external potential field…
We assume that markovian dynamics on a finite graph enjoys a gauge symmetry under local scalings of the probability density, derive the transformation law for the transition rates and interpret the thermodynamic force as a gauge potential.…
I give a quick overview of some of the theoretical background necessary for using modern non-equilibrium statistical physics to investigate the thermodynamics of computation. I first present some of the necessary concepts from information…
Entropy serves as a central observable in equilibrium thermodynamics. However, many biological and ecological systems operate far from thermal equilibrium. Here we show that entropy production can characterize the behavior of such…
Entropy is useful in statistical problems as a measure of irreversibility, randomness, mixing, dispersion, and number of microstates. However, there remains ambiguity over the precise mathematical formulation of entropy, generalized beyond…
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…
The original canonical ensemble formalism for the nonextensive entropy thermostatistics is reconsidered. It is shown that the unambiguous connection of the statistical mechanics with the equilibrium thermodynamics is provided if the…