April 2, 2003
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November 6, 2015
Based on quantum statistical mechanics and microscopic quantum dynamics, we prove Planck's and Kelvin's principles for macroscopic systems in a general and realistic setting. We consider a hybrid quantum system that consists of the thermodynamic system, which is initially in thermal equilibrium, and the "apparatus" which operates on the former, and assume that the whole system evolves autonomously. This provides a satisfactory derivation of the second law for macroscopic syst...
April 8, 1998
A unified presentation of the perturbation and variational methods for the generalized statistical mechanics based on Tsallis entropy is given here. In the case of the variational method, the Bogoliubov inequality is generalized in a very natural way following the Feynman proof for the usual statistical mechanics. The inequality turns out to be form-invariant with respect to the entropic index $q$. The method is illustrated with a simple example in classical mechanics. The fo...
October 10, 2000
An updated review [1] of nonextensive statistical mechanics and thermodynamics is colloquially presented. Quite naturally the possibility emerges for using the value of q-1 (entropic nonextensivity) as a simple and efficient manner to provide, at least for some classes of systems, some characterization of the degree of what is currently referred to as complexity [2]. A few historical digressions are included as well.
May 15, 2003
In this note it is shown that in his ``Comments'', Tsallis did not point out any flaws in the main criticism of my paper, namely, that the nonextensive q-entropy formalism fails to satisfy the zeroth law of thermodynamics. Details are also given of a rigorous thermodynamic proof which demonstrates that, contrary to Tsallis's assertion, the application of a nonextensive formalism to black-body radiation does not lead to the well known $T^4$ Stefan-Boltzman law.
December 29, 2005
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 article, we review two expositions of thermodynamics, one without reference to quantum theory, and the other quantum mechanical without probabilities of statistical mechanics. In the first, we show that entropy is an inherent property of any syst...
August 6, 2020
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 subs...
April 27, 2006
We describe recent progress towards deriving the Fundamental Laws of thermodynamics (the 0th, 1st and 2nd Law) from nonequilibrium quantum statistical mechanics in simple, yet physically relevant models. Along the way, we clarify some basic thermodynamic notions and discuss various reversible and irreversible thermodynamic processes from the point of view of quantum statistical mechanics.
November 16, 2000
In our recent letter [1] we discussed that thermodynamics is violated in quantum Brownian motion beyond the weak coupling limit. In his comment, Tasaki [2] derives an inequality for the relative entropy and claims, without making any dynamical assumption, that the Clausius inequality is valid, thus contradicting our statements [1]. Here we point out that the claim is unfunded, since the author did not properly identify the concept of heat. Tasaki also applies the inequality t...
March 24, 2000
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 processes for macroscopic systems. It is not necessary to assume a-priori concepts such as "heat", "hot and cold", "temperature". These are derivable from entropy, whose existence we derive from the basic assumptions. See cond-mat/9708200 and mat...
May 16, 2003
The nonextensive statistics based on the $q$-entropy $S_q=-\frac{\sum_{i=1}^v(p_i-p_i^q)}{1-q}$ has been so far applied to systems in which the $q$ value is uniformly distributed. For the systems containing different $q$'s, the applicability of the theory is still a matter of investigation. The difficulty is that the class of systems to which the theory can be applied is actually limited by the usual nonadditivity rule of entropy which is no more valid when the systems contai...