Related papers: A Noether Theorem for Markov Processes

Hunt's hypothesis (H) and the related Getoor's conjecture is one of the most important problems in the basic theory of Markov processes. In this paper, we investigate the invariance of Hunt's hypothesis (H) for Markov processes under two…

A discrete quantum process is represented by a sequence of quantum operations, which are completely positive maps that are not necessarily trace preserving. We consider quantum processes that are obtained by repeated iterations of a quantum…

This paper is devoted to studying symmetries of certain kinds of k-cosymplectic Hamiltonian systems in first-order classical field theories. Thus, we introduce a particular class of symmetries and study the problem of associating…

Any discrete quantum process is represented by a sequence of quantum channels. We consider ergodic quantum processes obtained by a map that takes the points along the trajectory of a discrete ergodic dynamical system to the space of quantum…

A generic non-integrable (unitary) out-of-equilibrium quantum process, when interrogated across many times, is shown to yield the same statistics as an (non-unitary) equilibrated process. In particular, using the tools of quantum stochastic…

The relation between quantum measurement and thermodynamically irreversible processes is investigated. The reduction of the state vector is fundamentally asymmetric in time and shows an observer-relatedness which may explain the double…

This paper is about the existence and regularity of the transition probability matrix of a nonhomogeneous continuous-time Markov process with a countable state space. A standard approach to prove the existence of such a transition matrix is…

Noether's celebrated theorem associating symmetry and conservation laws in classical field theory is adapted to allow for broken symmetry in geometric mechanics and is shown to play a central role in deriving and understanding the…

It is demonstrated that, making minimal changes in ordinary quantum mechanics, a reasonable irreversible quantum mechanics can be obtained. This theory has a more general spectral decompositions, with eigenvectors corresponding to unstable…

We exhibit two symmetries of one-dimensional Newtonian mechanics whereby a solution is built from the history of another solution via a generally nonlinear and complex potential-dependent transformation of the time. One symmetry intertwines…

We present a general quantum fluctuation theorem for the entropy production of an open quantum system coupled to multiple environments, not necessarily at equilibrium. Such a general theorem, when restricted to the weak-coupling and…

I propose a new and direct connection between classical mechanics and quantum mechanics where I derive the quantum mechanical propagator from a variational principle. This variational principle is Hamilton's modified principle generalized…

We develop a general framework for the steady-state response of dissipative quantum systems. We concretely derive three different, but equivalent, forms of the quantum response function. We discuss for each of them the role of the…

The classical quantization of the motion of a free particle and that of an harmonic oscillator on a double cone are achieved by a quantization scheme [M.C. Nucci, Theor. Math. Phys. 168 (2011) 994], that preserves the Noether point…

This paper considers a generalization of the notion of quantum observables in ontological models of quantum mechanics. Within this framework it is possible to construct physical models where quantum noncommutativity can arise dynamically.…

Noncommutativity of states and observables is a fundamental signature of quantum theory, and a minimal requirement for nonclassicality. We provide a universal necessary and sufficient condition for pairwise commutativity of quantum states…

We derive the fluctuation theorem for quantum-state statistics that can be obtained when we initially measure the total energy of a quantum system at thermal equilibrium, let the system evolve unitarily, and record the quantum-state data…

We develop a comprehensive framework for characterizing fluctuations in quantum transport and nonequilibrium thermodynamics using two complementary approaches: full counting statistics and first-passage times. Focusing on open quantum…

Thermodynamic systems typically conserve quantities ("charges") such as energy and particle number. The charges are often assumed implicitly to commute with each other. Yet quantum phenomena such as uncertainty relations rely on…

We clarify the relation between canonical and metric energy-momentum tensors. In particular, we show that a natural definition arises from Noether's Theorem which directly leads to a symmetric and gauge invariant tensor for electromagnetic…